What is the value of (tanƟ cosecƟ)2 -(sinƟ secƟ)2 (a) -1 (b) 0 (c) 1 (d) 2 - Maths - Some Applications of Trigonometry

Question

What is the value of (tanƟ cosecƟ)2
-(sinƟ secƟ)2

(a) -1 (b) 0 (c) 1 (d) 2

Ruchir Padhye · Accepted Answer

(tanƟ cosecƟ) = (tanƟ x 1/sinƟ) =
(sinƟ/cosƟ x 1/sinƟ) = (1/cosƟ) = secƟ
(sinƟ secƟ) = (sinƟ x 1/cosƟ) =
sinƟ/cosƟ = tanƟ

So substitution and evaluating, you get
(tanƟ cosecƟ)2 -(sinƟ secƟ)2
= (secƟ)2 -(tanƟ)2
= sec2Ɵ - tan2Ɵ
= 1