The general solution of ${\sin ^2}\,\,{\rm{\theta }}\,\,\sec \,\,{\rm{\theta }} + \sqrt 3 \,\,\tan \,\,{\rm{\theta }} = 0$ is

${\rm{\theta }} = n\pi + {\left( { - 1} \right)^{n + 1}}\,\,\frac{\pi }{3},\;\,{\rm{\theta }} = n\pi ,\;\,n \in I$

${\rm{\theta }} = n\pi + {\left( { - 1} \right)^{n + 1}}\,\,\frac{\pi }{3},\,\,n \in I$

${\rm{\theta }} = \frac{{n\pi }}{2},\,\;n \in I$

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JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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The general solution of

{\sin ^2}\,\,\mathrm{\theta }\,\,\sec \,\,\mathrm{\theta } + \sqrt 3 \,\,\tan \,\,\mathrm{\theta } = 0

View answer and explanation

Correct option: B

\mathrm{\theta } = n\pi ,\;\,n \in I

Option B (θ = nπ, n ∈ I) is correct because the equation simplifies to tan θ (sin θ + √3) = 0, and since sin θ + √3 ≠ 0, we have tan θ = 0, which gives θ = nπ.

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}

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\tan x

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