Question

trigonometric identities

tan^2Ө/sin^2Ө-1=tan^2Ө

Answer 1

LS = (sin^2 Ø/(sin^2 Ø cos^2 Ø) - 1
= (sin^2 Ø/(sin^2 Ø cos^2 Ø - (sin^2 Ø cos^2 Ø)/(sin^2 Ø cos^2 Ø)
= (sin^2 Ø - sin^2 Ø cos^2 Ø)/(sin^2 Ø cos^2 Ø)
= sin^2 Ø (1 - cos^2 Ø)/(sin^2 Ø cos^2 Ø
= sin^2 Ø (sin^2 Ø)/(sin^2 Ø cos^2 Ø)
= sin^2 Ø/cos^2 Ø
= tan^2 Ø
= RS