Question

(v) ( tan theta+cot theta)^ 2 -(tan theta-cot theta)^ 2 =4​

Answer 1

To Prove :

=> $(tanx+cotx)^2-(tanx-cotx)^2=4$

Proof :

By expanding we get,

=> $(tan^2x+cot^2x+2tanx.cotx)-(tan^2x+cot^2x-2tanx.cotx)$

=>  $tan^2x+cot^2x+2tanx.cotx-tan^2x-cot^2x+2tanx.cotx$

=>  $4tanx.cotx = 4$ (Because tanx.cotx = 1)