Question

Help me to prove that `tan^2A + cot^2 A + 2 = sec^2 A. csc^2 A` please? Thank you before.

`tan^2A + cot^2 A + 2 = sec^2 A. csc^2 A`

Answer 1

`LHS=tan^2A+cot^2A+2`

`=tan^2A+1+cot^2A+1`

`=sec^2A+csc^2A`

`=1/cos^2A+1/sin^2A`

`=(sin^2A+cos^2A)/(cos^2Asin^2A)`

`=1/(cos^2Asin^2A)`

`=sec^2Acsc^2A=RHS`