Question

if sin 0 +sin²0 =1 then prove that cos²0+cos⁴0=1​

Answer 1

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☸ 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!

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