Question

cos theta by 1 minus tan theta + sin theta by 1 - cot theta is equal to cos theta + sin theta prove

Answer 1

i hope it will help you

Answer 2

Answer:

The proof is explained step-wise below :

Step-by-step explanation:

$\textbf{To Prove : }\frac{\cos\theta}{1-\tan\theta}+\frac{\sin\theta}{1-\cot\theta}=\cos\theta+\sin\theta$

Proof : Taking LHS :

$=\frac{\cos\theta}{1-\tan\theta}+\frac{\sin\theta}{1-\cot\theta}\\\\= \frac{\cos\theta}{1-\tan\theta}-\frac{\sin\theta}{\cot\theta-1}\\\\=\frac{\cos\theta}{1-\frac{\sin\theta}{\cos\theta}}- \frac{\sin\theta}{1-\frac{\cos\theta}{\sin\theta}} \\\\=\frac{\cos^2\theta}{\cos\theta-\sin\theta}-\frac{\sin^2\theta}{\cos\theta-\sin\theta}\\\\=\frac{\cos^2 \theta-\sin^2\theta}{\cos\theta-\sin\theta}\\\\= \frac{(\cos\theta-\sin\theta)(\cos\theta+\sin\theta)}{(\cos\theta-\sin\theta)}\\\\={\cos\theta+\sin\theta}= R.H.S.$

Hence Proved