Question

If Sin θ + Sin2 θ = 1 , show that Cos2 θ + Cos4 θ = 1

Answer 1

Question:

If Sinθ + Sin²θ = 1 , show that Cos² θ + Cos^4θ = 1 ( Nice question ).

Given:

• Sinθ + Sin² = 1

To Prove:

• Cos²θ + cos^4θ = 1

Proof:

Given that,

• Sinθ + Sin²θ = 1

➡ Sinθ = 1 - Sin²θ

[ °.° Sin²θ + Cos²θ = 1 ]

[ .°. 1 - Sin²θ = Cos²θ ]

➡ Sinθ = Cos²θ _____________eqn. (1)

Now,

➡ Sinθ = Cos²θ [ From eqn. (1) ]

[ Squaring on both sides ; We get ]

➡ (Sinθ)² = (Cos²θ)²

➡ Sin²θ = Cos^4θ

➡ 1 - Cos²θ = Cos^4θ

➡ .°. Cos²θ + Cos^4θ = 1

Hence Proved!! ☺