Question

In a ∆ ABC, right angled at C and angle A = angle B,
(1) Is cos A = cos B.?
(2). Is tan A = tanB?​

Answer 1

Answer:

So, I'm proving this identity.. ( fundamental identity used : tan² A +1 = sec² A )

LHS = sec^4 A ( 1- sin^4 A ) -2 tan²A

= sec^4 A - ( sin^4A/cos^4A) - 2 tan² A

= sec^4 A - tan^4 A -2tan²A

= ( tan²A+1)² - tan^4A - 2 tan²A

= tan^4 A +2tan²A+1 - tan^4 A -2tan²A

= 1

= RHS

(Hence Proved )