JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

1 Easy

1 of 1

Analyzing +4 | -1

If the solution of the equation

\log _{\cos x} \cot x+4 \log _{\sin x}

\tan x=1, x \in\left(0, \frac{\pi}{2}\right)

, is

\sin ^{-1}\left(\frac{\alpha+\sqrt{\beta}}{2}\right)

, where

\alpha, \beta

are integers, then

\alpha+\beta

is equal to

View answer and explanation

Correct option: C

Option C (4) is correct because solving the logarithmic equation leads to a quadratic in sin(x), and the sum of the coefficients in the solution is 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)

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