Question

(sec^2theta-1)(1-cosec^2theta)=-1

Answer 1

Answer

(sec^2 Ø - 1)(1 - cosec^2 Ø)

= (1/cos^2 Ø - 1)(1 - 1/sin^2 Ø)

= (1 - cos^2 Ø/ cos^2 Ø)(sin^2 Ø - 1/ sin^2 Ø)

= (sin^2 Ø/ cos^2 Ø)(- cos^2 Ø/sin^2 Ø) [°.° sin^2 A = 1 - cos^2 A ; cos^2 A = 1 - sin^2 A]

= -1