Question

TRIGONOMETRY. only step by step answer no fake answer plz ​

Answer 1

     

Hey mate!!!

Here's the proof!!!

 

$\Rightarrow\ \boxed{LHS} \\ \\ \Rightarrow\ \boxed{\frac{\cot^2 A(\sec A-1)}{1+\sin A}+\frac{\sec^2A(\sin A-1)}{1+\sec A}} \\ \\ \\ \Rightarrow\ \boxed{\frac{\cot^2A(\sec A-1)(\sec A+1)+\sec^2A(\sin A-1)(\sin A+1)}{(1+\sec A)(1+\sin A)}} \\ \\ \\ \Rightarrow\ \boxed{\frac{\cot^2A(\sec^2 A-1)+\sec^2A(\sin^2 A-1)}{(1+\sec A)(1+\sin A)}} \\ \\ \\ \Rightarrow\ \boxed{\frac{\cot^2 A \cdot \tan^2A+\sec^2A \cdot \sin^2A-\sec^2A}{(1+\sec A)(1+\sin A)}}$

$\Rightarrow\ \boxed{\frac{1+\tan^2A-\sec^2A}{(1+\sin A)(1+\sec A)}} \\ \\ \\ \Rightarrow\ \boxed{\frac{1+(-1)}{(1+\sin A)(1+\sec A)}} \\ \\ \\ \Rightarrow\ \boxed{\frac{0}{(1+\sin A)(1+\sec A)}} \\ \\ \\ \Rightarrow\ \boxed{0} \\ \\ \Rightarrow\ \boxed{RHS}$

Hence proved!!!

Plz ask me if you've any doubt on my answer.

Thank you......

$\mathfrak{\#adithyasajeevan}$