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Question

The total number of solution of $sin to the power of 4 end exponent invisible function application x plus cos to the power of 4 end exponent invisible function application x equals sin invisible function application x cos invisible function application x$ in $blank open square brackets 0 comma blank 2 pi close square brackets blank$ is equal to

2
4
6
None of these

The correct answer is: 2

$sin to the power of 4 end exponent invisible function application x plus cos to the power of 4 end exponent invisible function application x equals sin invisible function application x cos invisible function application x$
$rightwards double arrow open parentheses sin to the power of 2 end exponent invisible function application x plus cos to the power of 2 end exponent invisible function application x close parentheses to the power of 2 end exponent minus 2 sin to the power of 2 end exponent invisible function application x cos to the power of 2 end exponent invisible function application x equals sin invisible function application x cos invisible function application x$
$rightwards double arrow 1 minus fraction numerator sin to the power of 2 end exponent invisible function application 2 x over denominator 2 end fraction equals fraction numerator sin invisible function application 2 x over denominator 2 end fraction$
$rightwards double arrow sin to the power of 2 end exponent invisible function application 2 x plus sin invisible function application 2 x minus 2 equals 0$
$rightwards double arrow open parentheses sin invisible function application 2 x plus 2 close parentheses open parentheses sin invisible function application 2 x minus 1 close parentheses equals 0$
$rightwards double arrow sin invisible function application 2 x equals 1$
$rightwards double arrow 2 x equals open parentheses 4 n plus 1 close parentheses fraction numerator pi over denominator 2 end fraction comma blank n element of Z$
$rightwards double arrow x equals open parentheses 4 n plus 1 close parentheses fraction numerator pi over denominator 4 end fraction comma n element of Z$
$equals fraction numerator pi over denominator 4 end fraction comma fraction numerator 5 pi over denominator 4 end fraction open parentheses because x element of open square brackets 0 comma blank 2 pi close square brackets close parentheses$
Thus, there are two solutions

Related Questions to study

$I f cos to the power of 2 end exponent invisible function application A plus cos to the power of 2 end exponent invisible function application B plus cos to the power of 2 end exponent invisible function application C equals 1 comma blank t h e n blank increment A B C blank i s$

$I f cos to the power of 2 end exponent invisible function application A plus cos to the power of 2 end exponent invisible function application B plus cos to the power of 2 end exponent invisible function application C equals 1 comma blank t h e n blank increment A B C blank i s$

If $cos invisible function application p theta plus cos invisible function application q theta equals 0 comma blank$ then the different values of $theta$ are in A.P. where the common difference is

If $cos invisible function application p theta plus cos invisible function application q theta equals 0 comma blank$ then the different values of $theta$ are in A.P. where the common difference is

If $x subscript 1 end subscript blank a n d blank x subscript 2 end subscript$ are the roots of the equation $e to the power of 2 end exponent blank. x to the power of ln invisible function application x end exponent equals x to the power of 3 end exponent blank w i t h blank x subscript 1 end subscript greater than x subscript 2 end subscript comma$ then

If $x subscript 1 end subscript blank a n d blank x subscript 2 end subscript$ are the roots of the equation $e to the power of 2 end exponent blank. x to the power of ln invisible function application x end exponent equals x to the power of 3 end exponent blank w i t h blank x subscript 1 end subscript greater than x subscript 2 end subscript comma$ then

parallel

$sec to the power of 2 end exponent invisible function application theta equals fraction numerator 4 x y over denominator open parentheses x plus y close parentheses to the power of 2 end exponent end fraction$ is true if and only if

$sec to the power of 2 end exponent invisible function application theta equals fraction numerator 4 x y over denominator open parentheses x plus y close parentheses to the power of 2 end exponent end fraction$ is true if and only if

Product of roots of the equation $fraction numerator log subscript 8 end subscript invisible function application open parentheses 8 divided by x to the power of 2 end exponent close parentheses over denominator open parentheses log subscript 8 end subscript invisible function application x close parentheses to the power of 2 end exponent end fraction equals 3$ is

Product of roots of the equation $fraction numerator log subscript 8 end subscript invisible function application open parentheses 8 divided by x to the power of 2 end exponent close parentheses over denominator open parentheses log subscript 8 end subscript invisible function application x close parentheses to the power of 2 end exponent end fraction equals 3$ is

The value of the expression $fraction numerator 2 open parentheses sin invisible function application 1 degree plus sin invisible function application 2 degree plus sin invisible function application 3 degree plus horizontal ellipsis plus sin invisible function application 89 degree close parentheses over denominator 2 open parentheses cos invisible function application 1 degree plus cos invisible function application 2 degree plus horizontal ellipsis plus cos invisible function application 44 degree close parentheses plus 1 end fraction$ equals

The value of the expression $fraction numerator 2 open parentheses sin invisible function application 1 degree plus sin invisible function application 2 degree plus sin invisible function application 3 degree plus horizontal ellipsis plus sin invisible function application 89 degree close parentheses over denominator 2 open parentheses cos invisible function application 1 degree plus cos invisible function application 2 degree plus horizontal ellipsis plus cos invisible function application 44 degree close parentheses plus 1 end fraction$ equals

parallel

In $blank increment A B C comma$ if $blank A equals 30 degree comma blank b equals 2 comma blank c equals square root of 3 plus 1 comma blank$ then $fraction numerator C minus B over denominator 2 end fraction blank$ is equal to

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$I f blank x comma blank y comma blank z blank a r e blank i n blank A. P comma blank t h e n fraction numerator sin invisible function application x minus sin invisible function application z over denominator cos invisible function application z minus cos invisible function application x end fraction blank i s blank e q u a l blank t o$

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The general value of $x$ satisfying the equation $2 cot to the power of 2 end exponent invisible function application x plus 2 square root of 3 cot invisible function application x plus 4 blank c o s e c blank x plus 8 equals 0$ is

The general value of $x$ satisfying the equation $2 cot to the power of 2 end exponent invisible function application x plus 2 square root of 3 cot invisible function application x plus 4 blank c o s e c blank x plus 8 equals 0$ is

parallel

If $open parentheses 21.4 close parentheses to the power of a end exponent equals open parentheses 0.00214 close parentheses to the power of b end exponent equals 100 comma$ then the value of $fraction numerator 1 over denominator b end fraction minus fraction numerator 1 over denominator b end fraction$ is

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The greatest value of $sin to the power of 4 end exponent invisible function application theta plus cos to the power of 4 end exponent invisible function application theta$ is

The greatest value of $sin to the power of 4 end exponent invisible function application theta plus cos to the power of 4 end exponent invisible function application theta$ is

parallel

If in a $increment A B C comma cos invisible function application 3 A plus cos invisible function application 3 B plus cos invisible function application 3 C equals 1 comma blank$ then one angle must be exactly equal to

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parallel

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