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JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

1 Easy

1 of 1

Application +4 | -1

If

\tan \,\,\left( {\pi \cos \,\,\theta } \right) = \cot \left( {\pi \,\sin \theta } \right),\;\,0 < \theta < \frac{{3\pi }}{4}

, then

\sin \left( {\theta + \frac{\pi }{4}} \right)

equals

View answer and explanation

Correct option: C

\frac{1}{{2\sqrt 2 }}

Option C (

\frac{1}{{2\sqrt 2 }}

) is correct because solving the given equation leads to

\sin(\theta + \frac{\pi}{4}) = \frac{1}{{2\sqrt 2 }}

.

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)

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