Question

if sin 0 + sin² 0=1, then cos² 0 +cos⁴ 0=
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Answer 1

Answer:

2 is your answer it's ok

Answer 2

Step-by-step explanation:

☸ Correct Question:

✒ sin θ + sin² θ = 1

Prove that cos² θ + cos⁴ θ = 1

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☸ How to solve?

For proving the above trignometric equation, we need to know only one identity i.e..

sin² θ + cos² θ = 1

❇ Some other identities:

sec² θ - tan² θ = 1

cosec² θ - cot² θ = 1

sin(A + B) = sinAcosB + sinBcosA

cos(A + B) = cosAcosB - sinAsinB

sin(A - B) = sinAcosB - sinBcosA

cos(A - B) = cosAcosB + sinAsinB

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☸ Solution:

We have,

sin θ + sin² θ = 1

This can be written as,

➙ sin θ + sin² θ = 1

➙ sin θ = 1 - sin² θ

[ From identity sin² θ + cos²θ = 1 ]

➙ sin θ = cos² θ

[ Squaring both sides ]

➙ (sin θ)² = (cos² θ)²

➙ sin² θ = cos⁴ θ

[ Again, using the same identity ]

➙ 1 - cos² θ = cos⁴ θ

➙ 1 = cos⁴ θ + cos² θ

➙ cos² θ + cos⁴ θ = 1

✒ Hence, proved!