Question

Sin 90-theta by 1+sin theta +cos theta by 1-cos 90 theta =2sec theta

Answer 1

you can see your answer

Answer 2

Answer:

The proof is explained step-wise below :

Step-by-step explanation:

To Prove :

$\frac{\sin(90-\theta)}{1+\sin\theta}+\frac{\cos\theta}{1-\cos(90-\theta)}=2\sec\theta$

Taking L.H.S.

$\frac{\sin(90-\theta)}{1+\sin\theta}+\frac{\cos\theta}{1-\cos(90-\theta)}\\\\ \implies \frac{\cos\theta}{1+\sin\theta}+\frac{\cos\theta}{1-\sin\theta}\\\\\implies \frac{\cos\theta(1-\sin\theta)+\cos\theta(1+\sin\theta)}{(1+\sin\theta)(1-\sin\theta)}\\\\\implies\frac{\cos\theta+\cos\theta}{1-\sin^2\theta}\\\\\implies \frac{2\cos\theta}{\cos^2\theta}\\\\\implies\frac{2}{\cos\theta}\\\\\implies 2\cdot\sec\theta$

= R.H.S.

Hence Proved