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in Trigonometry by (29.9k points)
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Prove that

(cos4x + sin4x) = 1/2(2 - sin22x)

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Best answer

To Prove: cos4x + sin4x = \(\frac{1}{2}\)(2 - sin22x)

Taking LHS,

= cos4x + sin4x

Adding and subtracting 2sin2x cos2x, we get

= cos4x + sin4x + 2sin2x cos2x – 2sin2x cos2x

We know that,

a2 + b2 + 2ab = (a + b)2

= (cos2x + sin2x) – 2sin2x cos2x

= (1) – 2sin2x cos2x [∵ cos2θ + sin2θ = 1]

= 1 – 2sin2x cos2x

Multiply and divide by 2, we get

= RHS

∴ LHS = RHS

Hence Proved

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