(i) (sec2 θ - 1)cot2 θ =1(ii) (sec2 θ - 1)(cosec2 θ - 1) = 1(

1.	(i) (sec2 θ - 1)cot2 θ =1(ii) (sec2 θ - 1)(cosec2 θ - 1) = 1(iii) (1- cos2 θ) sec2 θ = tan2 θ
Answer» (i) LHS = (sec² θ − 1) cot² θ = tan² θ × cot² θ (∵ sec ²θ − tan² θ = 1) = \(\frac{1}{cot^2θ}\times{cot^2θ}\) = 1 = RHS (ii) LHS = (sec² θ − 1)(cosec²θ − 1) = tan² θ × cot² θ (∵ sec² θ − tan² θ = 1and cosec² θ − cot² θ = 1) = \(tan^2θ \times\frac{1}{tan^2θ}\) = 1 = RHS (iii) LHS = (1 − cos² θ) sec² θ = sin² θ × sec² θ (∵ sin² θ + cos² θ = 1) = \(sin^2θ \times\frac{1}{cos^2θ}\) = \(\frac{sin^2θ}{cos^2θ}\) = tan²θ = RHS

(i) (sec2 θ - 1)cot2 θ =1(ii) (sec2 θ - 1)(cosec2 θ - 1) = 1(iii) (1- cos2 θ) sec2 θ = tan2 θ

Answer»

(i) LHS = (sec² θ − 1) cot² θ

= tan² θ × cot² θ (∵ sec ²θ − tan² θ = 1)

= \(\frac{1}{cot^2θ}\times{cot^2θ}\)

= 1

= RHS

(ii) LHS = (sec² θ − 1)(cosec²θ − 1)

= tan² θ × cot² θ (∵ sec² θ − tan² θ = 1and cosec² θ − cot² θ = 1)

= \(tan^2θ \times\frac{1}{tan^2θ}\)

= 1

= RHS

(iii) LHS = (1 − cos² θ) sec² θ

= sin² θ × sec² θ (∵ sin² θ + cos² θ = 1)

= \(sin^2θ \times\frac{1}{cos^2θ}\)

= \(\frac{sin^2θ}{cos^2θ}\)

= tan²θ

= RHS