Question

tan^2 A / tan^2 A -1 + cosec^2 A / sec^2 A - cosec^2 A = 1 / sin^2 A - cos^2 A

Answer 1

Answer:

tan^2 A / tan^2 A -1 + cosec^2 A / sec^2 A - cosec^2 A = 1 / sin^2 A - cos^2 A

Answer 2

Soln,

L.H.S.= tan^2 A / tan^2 A -1 + cosec^2 A / sec^2 A - cosec^2 A

=(sin^2 A/cos^2 A)/{(sin^2 A/cos^2 A)-1}+ (1/sin^2 A)/{(1/cos^2 A)-(1/sin^2 A)}

=sin^2 A/cos^2 A(sin^2 A-cos^2 A)/cos^2 A + cos^2 A/ sin^2A(sin^2 A-cos^2 A)/sin^2A

=sin^2 A/sin^2 A-cos^2A + cos^2 A/ sin^2 A-cos^2 A

=sin^2 A+cos^2 A/ sin^2 A-cos^2 A

=1 / sin^2 A - cos^2 A