Question

Prove that cot²(90-θ)/ tan²θ)-1 + cosec² θ/ sec² θ - cosec² θ = 1/ sin² θ - cos² θ

Answer 1

Explanation:

Trigonometry is the study of the relationship between the sides and angles of a triangle.

We know that :

i) sin² θ + cos² θ = 1 , ii) 1 + tan² θ = sec² θ , iii) cot² θ +1 = cosec² θ.

SOLUTION :

Given :

sec⁴ θ – sec²θ = tan⁴θ + tan²θ

L.H.S

= sec⁴ θ – sec²θ

= sec² θ (sec² θ -1)

= (1 + tan² θ) (1 + tan² θ -1) …..[ sec² θ = 1 + tan² θ ]

= (1 + tan² θ) ( tan² θ)

= tan²θ + tan⁴θ

L.H.S = R.H.S

bluecore2665,

thanks