Question

please prove this identity ​

Answer 1

To prove---->

Sec⁴θ - Sec²θ = tan²θ + tan⁴θ

Proof------> LHS

= Sec⁴θ - Sec²θ

Taking Sec²θ common from both the terms

= Sec²θ ( Sec²θ - 1 )

We know that ,

1 + tan²θ = Sec²θ , using it , we get,

= Sec²θ ( 1 + tan²θ - 1 )

= Sec²θ ( tan²θ )

Using , Sec²θ = 1 + tan²θ , we get ,

= ( 1 + tan²θ ) tan²θ

= tan²θ + tan²θ tan²θ

= tan²θ + tan⁴θ

Additional identity---->

1) Sin²θ + Cos²θ = 1

2) 1 + tan²θ = Sec²θ

3) 1 + Cot²θ = Cosec²θ