The solution set of the inequation ${\log _{1/2}}\sin x > {\log _{1/2}}\cos x$ in $\left[ {0,\;\,2\pi } \right]$, is

$\left( {0,\;\,\pi /2} \right)$

$\left( { - \pi /4,\,\pi /4} \right)$

JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Analyzing +4 | -1

The solution set of the inequation

{\log _{1/2}}\sin x > {\log _{1/2}}\cos x

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

, is

View answer and explanation

Correct option: C

\left( {0,\,\,\pi /4} \right)

Option C is correct because it correctly identifies the interval where sin x < cos x and both sin x and cos x are positive within the given range [0, 2π].

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The number of solutions of the equation

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

is The number of ordered pairs

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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]

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

is If

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