Question

sin theta + sin² theta =1,then cos² theta + cos⁴ theta is equal to​

Answer 1

sin theta + sin² theta =1,then cos² theta + cos⁴ theta is equal to 1

Answer 2

Answer:

1

Step-by-step explanation:

Given, sinθ + sin²θ =1

=> sinθ = 1 - sin²θ

=> sinθ = cos²θ  _____ $\boxed {\mathrm{sin^2 \theta + cos^2 \theta = 1}}$

sinθ = cos²θ -----(1)

Now, Squaring on both sides, we get

sin²θ = cos⁴θ ----- (2)

Now, Question is what is the value of cos² theta + cos⁴ theta

cos²θ + cos⁴θ = sinθ + sin²θ _____ [from (1) and (2)]

=> sinθ + sin²θ =1 (from question)

Hence, cos²θ + cos⁴θ = 1

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