Question

prove that (1+ tanAtanB)² + (tanA - tanB)² = sec²Asec²B​

Answer 1

Answer:

Step-by-step explanation:

(1 + TanATanB)² + (TanA - TanB)²

= 1 + 2TanATanB + Tan²ATan²B + Tan²A + Tan²B - 2TanATanB

= (1 + Tan²A) + Tan²B( 1 + Tan²A)

= (1 + Tan²A)(1 + Tan²B)

= Sec²A Sec²B

= R.H.S

Hence Proved.