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Question

f in $increment A B C comma blank 8 R to the power of 2 end exponent equals a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent comma$ then the triangle $A B C$ is

Right angled
Isosceles
Equilateral
None of these

The correct answer is: Right angled

We have $8 R to the power of 2 end exponent equals a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent$
$equals 4 R to the power of 2 end exponent open parentheses sin to the power of 2 end exponent invisible function application A plus sin to the power of 2 end exponent invisible function application B plus sin to the power of 2 end exponent invisible function application C close parentheses$
$rightwards double arrow sin to the power of 2 end exponent invisible function application A plus sin to the power of 2 end exponent invisible function application B plus sin to the power of 2 end exponent invisible function application C equals 2$
$rightwards double arrow 1 minus cos to the power of 2 end exponent invisible function application A plus 1 minus cos to the power of 2 end exponent invisible function application B plus sin to the power of 2 end exponent invisible function application C equals 2$
$rightwards double arrow open parentheses cos to the power of 2 end exponent invisible function application A minus sin to the power of 2 end exponent invisible function application C close parentheses plus cos to the power of 2 end exponent invisible function application B equals 0$
$rightwards double arrow cos invisible function application open parentheses A plus C close parentheses cos invisible function application open parentheses A minus C close parentheses plus cos to the power of 2 end exponent invisible function application B equals 0$
$rightwards double arrow negative cos invisible function application B open square brackets cos invisible function application open parentheses A minus C close parentheses minus cos invisible function application B close square brackets equals 0$
$rightwards double arrow negative cos invisible function application B open square brackets cos invisible function application open parentheses A minus C close parentheses plus cos invisible function application open parentheses A plus C close parentheses close square brackets equals 0$
$rightwards double arrow negative 2 cos invisible function application A cos invisible function application B cos invisible function application C equals 0$
$rightwards double arrow cos invisible function application A equals 0$ or $cos invisible function application B equals 0 blank$ or $cos invisible function application C equals 0$
$rightwards double arrow A equals fraction numerator pi over denominator 2 end fraction blank o r blank B equals fraction numerator pi over denominator 2 end fraction blank o r blank C equals fraction numerator pi over denominator 2 end fraction$

Related Questions to study

The total number of solutions of $open vertical bar cot invisible function application x close vertical bar equals cot invisible function application x plus fraction numerator 1 over denominator sin invisible function application x end fraction comma blank x element of open square brackets 0 comma blank 3 pi close square brackets$ is equal to

The total number of solutions of $open vertical bar cot invisible function application x close vertical bar equals cot invisible function application x plus fraction numerator 1 over denominator sin invisible function application x end fraction comma blank x element of open square brackets 0 comma blank 3 pi close square brackets$ is equal to

If the inequality $sin to the power of 2 end exponent invisible function application x plus a cos invisible function application x plus a to the power of 2 end exponent greater than 1 plus cos invisible function application x$ holds for any $x element of R comma$ then the largest negative integral value of $a$ is

If the inequality $sin to the power of 2 end exponent invisible function application x plus a cos invisible function application x plus a to the power of 2 end exponent greater than 1 plus cos invisible function application x$ holds for any $x element of R comma$ then the largest negative integral value of $a$ is

$fraction numerator sin invisible function application 3 theta plus sin invisible function application 5 theta plus sin invisible function application 7 theta plus sin invisible function application 9 theta over denominator cos invisible function application 3 theta plus cos invisible function application 5 theta plus cos invisible function application 7 theta plus cos invisible function application 9 theta end fraction blank i s blank e q u a l blank t o$

$fraction numerator sin invisible function application 3 theta plus sin invisible function application 5 theta plus sin invisible function application 7 theta plus sin invisible function application 9 theta over denominator cos invisible function application 3 theta plus cos invisible function application 5 theta plus cos invisible function application 7 theta plus cos invisible function application 9 theta end fraction blank i s blank e q u a l blank t o$

parallel

If $a to the power of 4 end exponent blank. b to the power of 5 end exponent equals 1 comma$ then the value of $log subscript a end subscript invisible function application open parentheses a to the power of 5 end exponent b to the power of 4 end exponent close parentheses$ equals

If $a to the power of 4 end exponent blank. b to the power of 5 end exponent equals 1 comma$ then the value of $log subscript a end subscript invisible function application open parentheses a to the power of 5 end exponent b to the power of 4 end exponent close parentheses$ equals

If $open parentheses x plus 1 close parentheses to the power of log subscript 10 end subscript invisible function application open parentheses x plus 1 close parentheses end exponent equals 100 open parentheses x plus 1 close parentheses comma$ then

If $open parentheses x plus 1 close parentheses to the power of log subscript 10 end subscript invisible function application open parentheses x plus 1 close parentheses end exponent equals 100 open parentheses x plus 1 close parentheses comma$ then

The sum of all the solution of $cot invisible function application theta equals sin invisible function application 2 theta comma blank open parentheses theta not equal to n pi comma n blank i n t e g e r close parentheses comma blank 0 less or equal than theta less or equal than pi blank$ is

The sum of all the solution of $cot invisible function application theta equals sin invisible function application 2 theta comma blank open parentheses theta not equal to n pi comma n blank i n t e g e r close parentheses comma blank 0 less or equal than theta less or equal than pi blank$ is

parallel

The number of solutions of the equation $sin to the power of 3 end exponent invisible function application x cos invisible function application x plus sin to the power of 2 end exponent invisible function application x cos to the power of 2 end exponent invisible function application x plus sin invisible function application x cos to the power of 3 end exponent invisible function application x equals 1 comma blank$ in the interval $open square brackets 0 comma blank 2 pi close square brackets comma blank$ is

The number of solutions of the equation $sin to the power of 3 end exponent invisible function application x cos invisible function application x plus sin to the power of 2 end exponent invisible function application x cos to the power of 2 end exponent invisible function application x plus sin invisible function application x cos to the power of 3 end exponent invisible function application x equals 1 comma blank$ in the interval $open square brackets 0 comma blank 2 pi close square brackets comma blank$ is

If $a comma blank b blank$ and $blank c$ are the sides of a triangle, then the minimum value of $fraction numerator 2 a over denominator b plus c minus a end fraction plus fraction numerator 2 b over denominator c plus a minus b end fraction plus fraction numerator 2 c over denominator a plus b minus c end fraction$ is

If $a comma blank b blank$ and $blank c$ are the sides of a triangle, then the minimum value of $fraction numerator 2 a over denominator b plus c minus a end fraction plus fraction numerator 2 b over denominator c plus a minus b end fraction plus fraction numerator 2 c over denominator a plus b minus c end fraction$ is

Let $alpha blank a n d blank beta$ be such that $pi less than alpha minus beta less than 3 pi.$ If $sin invisible function application alpha plus sin invisible function application beta equals negative fraction numerator 21 over denominator 65 end fraction blank a n d cos invisible function application alpha plus cos invisible function application beta equals negative fraction numerator 17 over denominator 65 end fraction comma$ then the value of $cos invisible function application fraction numerator alpha minus beta over denominator 2 end fraction$ is

Let $alpha blank a n d blank beta$ be such that $pi less than alpha minus beta less than 3 pi.$ If $sin invisible function application alpha plus sin invisible function application beta equals negative fraction numerator 21 over denominator 65 end fraction blank a n d cos invisible function application alpha plus cos invisible function application beta equals negative fraction numerator 17 over denominator 65 end fraction comma$ then the value of $cos invisible function application fraction numerator alpha minus beta over denominator 2 end fraction$ is

parallel

One of the general solutions of $4 sin to the power of 4 end exponent invisible function application x plus cos to the power of 4 end exponent invisible function application x equals 1$ is

One of the general solutions of $4 sin to the power of 4 end exponent invisible function application x plus cos to the power of 4 end exponent invisible function application x equals 1$ is

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Which of the following is not the value of $sin invisible function application 27 degree minus cos invisible function application 27 degree ?$

The sum of all roots of $sin invisible function application open parentheses pi log subscript 3 end subscript invisible function application open parentheses fraction numerator 1 over denominator x end fraction close parentheses close parentheses equals 0$ in $blank open parentheses 0 comma blank 2 pi close parentheses$ is

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parallel

If $sin invisible function application theta subscript 1 end subscript plus sin invisible function application theta subscript 2 end subscript plus sin invisible function application theta subscript 3 end subscript equals 3 comma$ then $cos invisible function application theta subscript 1 end subscript plus cos invisible function application theta subscript 2 end subscript plus cos invisible function application theta subscript 3 end subscript$ is equal to

If $sin invisible function application theta subscript 1 end subscript plus sin invisible function application theta subscript 2 end subscript plus sin invisible function application theta subscript 3 end subscript equals 3 comma$ then $cos invisible function application theta subscript 1 end subscript plus cos invisible function application theta subscript 2 end subscript plus cos invisible function application theta subscript 3 end subscript$ is equal to

The set of values of $theta$ satisfying the inequation $2 sin to the power of 2 end exponent invisible function application theta minus 5 sin invisible function application theta plus 2 greater than 0$ , where $0 less than theta less than 2 pi$ , is

The set of values of $theta$ satisfying the inequation $2 sin to the power of 2 end exponent invisible function application theta minus 5 sin invisible function application theta plus 2 greater than 0$ , where $0 less than theta less than 2 pi$ , is

In any triangle $A B C comma fraction numerator a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent over denominator R to the power of 2 end exponent end fraction$ has the maximum value of

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parallel

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