Question

Prove the following trigonometric identities:
(sec²θ-1)(cosec²θ-1)=1

Answer 1

Answer:

Is it correct? I am not sure.....

Answer 2

To prove ----->

( Sec²θ - 1 ) ( Cosec²θ - 1 ) = 1

Proof-----> We know that ,

1 + tan²θ = Sec²θ

=> tan²θ = Sec²θ - 1

We know that ,

1 + Cot²θ = Cosec²θ

=> Cot²θ = Cosec²θ - 1

LHS = ( Sec²θ - 1 ) ( Cosec²θ - 1 )

Putting Sec²θ - 1 = tan²θ and Cosec²θ - 1 = Cot²θ , we get ,

= ( tan²θ ) ( Cot²θ )

= ( tan²θ ) ( 1 / tan²θ )

= 1 = RHS

Additional information------->

1) Sin²θ + Cos²θ = 1

2) Sin²θ = 1 - Cos²θ

3) Cos²θ = 1 - Sin²θ

4) 1 + tan²θ = Sec²θ

5) tan²θ = Sec²θ - 1

6) Sec²θ - tan²θ = 1

7) 1 + Cot²θ = Cosec²θ

8) Cot²θ = Cosec²θ - 1

9) Cosec²θ - Cot²θ = 1