Question

tan square theta - sin square theta = sin four theta . sec square theta prove the following with full explaination​....

Answer 1

Answer:

Tan²θ - Sin²θ  = Sin⁴θ . Sec²θ

Step-by-step explanation:

Tan square theta - sin square theta = sin four theta . sec square theta

Tan²θ - Sin²θ  = Sin⁴θ . Sec²θ

LHS

= Tan²θ - Sin²θ

Using Sin²θ = Cosθ Tanθ

= Tan²θ - Cos²θ Tan²θ

Taking common Tan²θ

= Tan²θ(1 - Cos²θ)

Using 1 - Cos²θ = Sin²θ

= Tan²θ . Sin²θ

using Tanθ = Sinθ/Cosθ

= (Sin²θ/Cos²θ) . Sin²θ

= Sin⁴θ /Cos²θ

using 1/Cosθ = Secθ

= Sin⁴θ . Sec²θ

= RHS

QED

Proved

Tan²θ - Sin²θ  = Sin⁴θ . Sec²θ