Question

Prove:
$\sin \theta \cos (90-\theta )+\cos \theta \sin (90-\theta )=1$

Answer 1

We have

$\sin \theta \cos (90-\theta )+\cos \theta \sin (90-\theta )\dots \dots \left(1\right)$

We know that, $\cos (90-\theta )=\sin \theta$.

and $\sin (90-\theta )=\cos \theta$

From $\left(1\right)$, we get

$\Rightarrow \sin \theta \sin \theta +\cos \theta \cos \theta ={\sin }^2\theta +{\cos }^2\theta =1$