Question

(sin alpha +cos alpha)(tan alpha+cot alpha) = sec alpha +cosec alpha

Answer 1

hope you understand the solution

Answer 2

Step-by-step explanation:

Since we have given that

$(\sin \alpha+\cos \alpha)(\tan \alpha+\cot \alpha)=\sec \alpha+\cosec \alpha$

We need to prove it .

From L.H.S. ,

$(\sin \alpha+\cos \alpha)(\tan \alpha+\cot \alpha)\\\\=(\sin \alpha+\cos \alpha)(\frac{\sin \alpha}{\cos \alpha}+\frac{\cos\alpha}{\sin \alpha})\\\\=(\sin \alpha+\cos \alpha)(\frac{\sin^2\alpha+\cos^2\alpha}{\sin \alpha \cos \alpha})\\\\=(\sin \alpha+\cos \alpha)(\frac{1}{\sin \alpha \cos \alpha})\\\\=(\frac{\sin \alpha}{\sin \alpha \cos \alpha})+(\frac{\cos \alpha}{\sin \alpha \cos \alpha})\\\\=\sec \alpha+cosec\ \alpha$

Hence, Proved.