If the solutions for ${\rm{\theta }},\,\cos p{\rm{\theta }} + \cos q{\rm{\theta }} = 0,\;\,p > 0,\;\,q > 0$ are in AP, then the numerically smallest common difference of AP is

$\frac{\pi }{{2\left( {p + q} \right)}}$

JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Application +4 | -1

If the solutions for

\mathrm{\theta },\,\cos p\mathrm{\theta } + \cos q\mathrm{\theta } = 0,\;\,p > 0,\;\,q > 0

are in AP, then the numerically smallest common difference of AP is

View answer and explanation

Correct option: B

\frac{{2\pi }}{{p + q}}

Option B (

\frac{{2\pi }}{{p + q}}

) is correct because it represents the smallest common difference of the arithmetic progression formed by the solutions of the given trigonometric equation.

More Questions from TRIGONOMETRIC EQUATIONS

Practice All Chapter MCQs →

The number of solutions of the equation

\sin \,\,x\,\,\;cos\,\,3x = \sin \,\,3x\,\,\cos \,\,5x

\left[ {0,\;\,\frac{\pi }{2}} \right]

is The number of ordered pairs

\left( {x,\,y} \right)

where

x,\,\,y \in \left[ {0,10} \right]

satisfying

\left( {\sqrt {{{\sin }^2} - \sin \,\,x + \frac{1}{2}} } \right){2^{{{\sec }^2}y}}\,\, \cdot \,\, \le 1

is Statement I: If slope of the tangent line is zero, then tangent line is perpendicular to the

\mathrm{X}

-axis.

Statement II: If

\theta \rightarrow \frac{\pi}{2}

, then tangent line is parallel to the Y-axis.
If

\sin x+\cos x=\frac{\sqrt{7}}{2}

, where

x \in\left[0, \frac{\pi}{4}\right]

, then

\tan \frac{x}{2}

is equal to The value of

\tan \frac{\pi}{5}+2 \tan \frac{2 \pi}{5}+4 \cot \frac{4 \pi}{5}

is If

0 < x < \pi

and

\cos x+\sin x=\frac{1}{2}

, then

\tan x

is equal to