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Maths-

General

Easy

Question

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

$\frac{π}{p + q}$
$\frac{π}{p - q}$
$\frac{2 π}{p + q}$
$\frac{3 π}{p \pm q}$

The correct answer is: $fraction numerator 2 pi over denominator p plus q end fraction$

$cos invisible function application p theta equals negative cos invisible function application q theta equals cos invisible function application open parentheses pi minus q theta close parentheses$
$rightwards double arrow p theta equals 2 n pi plus-or-minus open parentheses pi minus q theta close parentheses$
$rightwards double arrow open parentheses p minus-or-plus q close parentheses theta equals open parentheses 2 n plus-or-minus 1 close parentheses pi$
$rightwards double arrow theta equals fraction numerator open parentheses 2 n plus-or-minus 1 close parentheses pi over denominator open parentheses p minus-or-plus q close parentheses end fraction comma blank n element of Z$
$rightwards double arrow theta equals fraction numerator r pi over denominator p plus-or-minus q end fraction$ , where $blank r equals negative 3 comma blank minus 1 comma blank 1 comma blank 3 comma blank horizontal ellipsis$
$rightwards double arrow theta equals horizontal ellipsis comma blank fraction numerator negative 3 pi over denominator p plus-or-minus q end fraction comma blank fraction numerator negative pi over denominator p plus-or-minus q end fraction comma blank fraction numerator pi over denominator p plus-or-minus q end fraction comma blank fraction numerator 3 pi over denominator p plus-or-minus q end fraction comma blank horizontal ellipsis$
Shown above is an A.P. of common difference $fraction numerator 2 pi over denominator p plus-or-minus q end fraction$

Related Questions to study

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

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

parallel

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

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

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

parallel

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

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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parallel

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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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Maths-General

$I f tan invisible function application x equals n tan invisible function application y comma blank n element of R to the power of plus end exponent comma$ then the maximum value of $s e c to the power of 2 end exponent open parentheses x minus y close parentheses$ is equal to

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parallel

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