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Solve each trigonometric equation for θ with 0 ≤ θ <2π. . cot(π/2- θ) = sinθ

User Maslan
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1 Answer

3 votes

Answer:
\theta=0, \pi

Explanation:

Note
\cot \left((\pi)/(2) -\theta \right)=\tan \theta.


\tan \theta=\sin \theta\\\\(\sin \theta)/(\cos \theta)=\sin \theta\\\\\sin \theta \left((1)/(\cos \theta)-1 \right)=0\\\\\implies \sin \theta=0, (1)/(\cos \theta)-1=0\\\\\sin \theta=0 \implies \theta=0, \pi\\\\(1)/(\cos \theta)-1=0 \implies \cos \theta=1 \implies \theta=0\\\\\therefore \theta=0, \pi

User DannyNiu
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