Question

(1- cos A)(1+ sec A) = tan A sin A

Prove this....

Answer 1

open the bracket
when u will multiply,,,you will get,
1-cosA+secA-1
then please refer to image
after that
secA-cosA
convert secA into cosA
1/cosA-CosA

Answer 2

Given LHS =  (1 - cosA)(1 + secA) 

= $(1 - cos A)(1 + \frac{1}{cosA} )$

= $(1 - cosA) (\frac{cosA+1}{cosA})$

= $\frac{(1-cosA)(1+cosA)}{cosA}$

= $\frac{1-cos^2A}{cosA}$

= $\frac{sin^2A}{cosA}$

= $sinA * \frac{sinA}{cosA}$

= sinA * tanA.


Hope this helps!