Question

Prove cos(pi/2 -theta)=sin theta (I will give 100 points please help ASAP)

Answer 1

`\cos(\alpha - \beta)= \cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cos\left( (\pi )/(2)-\theta \right)~~ = ~~\sin(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \cos\left( (\pi )/(2)-\theta \right)\implies \cos\left( (\pi )/(2)\right)\cos(\theta)~~ + ~~\sin\left( (\pi )/(2)\right)\sin(\theta) \\\\\\ \text{\LARGE 0}\cdot \cos(\theta)~~ + ~~\text{\LARGE 1}\cdot \sin(\theta)\implies 0+\sin(\theta )\implies \sin(\theta )`

Answer 2

cos(π/2 - θ) = cos(π/2) cosθ + sin(π/2) sinθ = sinθ

Explanation:

Explanation is in the attachment.