Question

if sin theta+sin²theta=1 then prove that cos²theta+cos^4theta=1​

Answer 1

i wrote it down to help u :)

Answer 2

Answer:

sinθ + sin²θ = 1

⇒ sinθ + sin²θ = sin²θ + cos²θ

⇒ sinθ = cos²θ

Now,

    cos²θ + cos⁴θ

 = cos²θ ( 1 + cos²θ )

 = sinθ ( 1 + sinθ )

 = sinθ + sin²θ

 = 1

Hence, proved that cos²θ + cos⁴θ = 1

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