Question

answer plz..this prove I'll be grateful​

Answer 1

         

$\ \ \ \ \ \boxed{ LHS } \\ \\ \\ \Rightarrow\ \boxed{\frac{\cot\theta}{\csc\theta+1}+\frac{\csc\theta+1}{\cot\theta}} \\ \\ \\ \Rightarrow\ \boxed{\frac{\tan\theta \cdot \cot\theta}{\tan\theta(\csc\theta+1)}+\frac{\tan\theta(\csc\theta+1)}{\tan\theta \cdot \cos\theta}} \\ \\ \\ \Rightarrow\ \boxed{\frac{1}{\sec\theta+\tan\theta}+\sec\theta+\tan\theta} \\ \\ \\ \Rightarrow\ \boxed{\frac{1+(\sec\theta+\tan\theta)^2}{\sec\theta+\tan\theta}}$

$\Rightarrow\ \boxed{\frac{1+\sec^2\theta+2\sec\theta \cdot\tan\theta+\tan^2\theta}{\sec\theta+\tan\theta}} \\ \\ \\ \Rightarrow\ \boxed{\frac{\sec^2\theta+\sec^2\theta+2\sec\theta \cdot\tan\theta}{\sec\theta+\tan\theta}} \\ \\ \\ \Rightarrow\ \boxed{\frac{2\sec^2\theta+2\sec\theta \cdot \tan\theta}{\sec\theta+\tan\theta}} \\ \\ \\ \Rightarrow\ \boxed{\frac{2\sec\theta(\sec\theta+\tan\theta)}{\sec\theta+\tan\theta}} \\ \\ \\ \Rightarrow\ \boxed{2\sec\theta} \\ \\ \\ \Rightarrow\ \boxed{ RHS }$

$Hence proved! \\ \\ \\ Hope this helps. Plz ask me if you've any doubts. \\ \\ \\ Thank you. :-)) \\ \\ \\ \\ \\ \#adithyasajeevan$