Question

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

Answer 1

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`