Question

if sin theta + sin sq theta =1
show that
cos sq theta + cos 4 theta = 1​

Answer 1

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Answer 2

Step-by-step explanation:

Given-----> Sinθ + Sin²θ = 1

To prove -----> Cos²θ + Cos⁴θ = 1

Proof-----> ATQ,

Sinθ + Sin²θ = 1

=> Sinθ = 1 - Sin²θ

We know that, Cos²θ = 1 - Sin²θ , applying it , we get,

=> Sinθ = Cos²θ

Now ,

LHS = Cos²θ + Cos⁴θ

= Cos²θ + ( Cos²θ )²

Putting , Cos²θ = Sinθ in second term only , we get,

= Cos²θ + ( Sinθ )²

= Cos²θ + Sin²θ

We know that , Sin²θ + Cos²θ = 1

= 1 = RHS

Additional information---->

1) Sin²θ + Cos²θ = 1

2) 1 + tan²θ = Sec²θ

3) 1 + Cot²θ = Cosec²θ