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JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Application +4 | -1

If

\tan \alpha=\frac{1}{7}

and

\sin \beta=\frac{1}{\sqrt{10}}

, where

0 < \alpha, \beta < \frac{\pi}{2}

, then

2 \beta

is equal to

View answer and explanation

Correct option: A

\frac{\pi}{4}-\alpha

Option A (

\frac{{\pi}}{{4}} - \alpha

) is correct because by calculating

\sin 2\beta

and then

\tan(\alpha + 2\beta)

, we find that

\alpha + 2\beta = \frac{{\pi}}{{4}}

.

More Questions from TRIGONOMETRIC EQUATIONS

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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)

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

\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}

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

\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}

0 < x < \pi

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

\tan x