What is the general solution of the equation \cot \theta+\tan \theta=2 ?

\theta=\frac{n \pi}{2}+\frac{\pi}{8}

\theta=\frac{n \pi}{2}+\frac{\pi}{4}

\theta=\frac{n \pi}{2}+\frac{\pi}{6}

NIMCET 2025 Paper

Section: Mathematics

Question : 35 of 120

Marks: +1, -0

What is the general solution of the equation

\cot θ+\tan θ=2 ?

Solution:

\cot θ+\tan θ=\;{\cos }/{ sin \;}+\;{ sin \;}/{\cos }=\;{ sin \;^2+\cos ^2}/{ sin \;\cos }=\;{1}/{ sin \;θ \cos θ}

Given:

\;{1}/{ sin \;θ \cos θ}=2 ⇒ sin \;θ \cos θ=\;{1}/{2}

But

sin \;θ \cos θ=\;{1}/{2} sin \;2 θ

So:

\;{1}/{2} sin \;2 θ=\;{1}/{2} ⇒ sin \;2 θ=1

Thus:

2 θ=\;{π}/{2}+2 π n ⇒ θ=\;{π}/{4}+n π

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