Question

Solve tan^2x + cot^2x + sec^2x + sin^2x + cos^2x + cosec^2x is

Answer 1

tan^2x= sec^2x -1

cot^2x = cosec^2 x -1

sin^2x = 1-cos^2x

so.......

(sec^2x -1) + (cosec^2x -1) + (1-cos^2x) +sec^2x + cos ^2x + cosec^2x

= 2sec^2x + 2cosec^2x -1

=2/cos^2x  +  2/sin^2x - 1

=2(1)/Sin^2(2x) -1

= 2cosec^2(2x) -1