JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Application +4 | -1

4 \cos \theta+5 \sin \theta=1

and

\alpha

satisfy equation and

\alpha \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)

then, value of

\tan \alpha

View answer and explanation

Correct option: B

\frac{\sqrt{10}-10}{12}

The correct answer is B;

\frac{{\sqrt{{10}} - 10}}{{12}}

. It involves using trigonometric identities to convert the given equation into a quadratic equation in terms of

\tan(\theta/2)

, solving for

\tan(\theta/2)

, and then finding

\tan(\alpha)

More Questions from TRIGONOMETRIC EQUATIONS

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

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

\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

\mathrm{X}

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

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

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

\tan \frac{x}{2}

\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