Question

11. Prove that cos^4x =3/8 +1/2 cos2x + 1/8 cos4x

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Answer 1

Answer:

Let us consider the LHS cos 4x As we know, cos 2x = 2 cos2 x – 1 Therefore, cos 4x = 2 cos2 2x – 1 = 2(2 cos2 2x – 1)2 – 1 = 2[(2 cos2 2x)2 + 12 – 2 × 2 cos2 x] – 1 = 2(4 cos4 2x + 1 – 4 cos2 x) – 1 = 8 cos4 2x + 2 – 8 cos2 x – 1 = 8 cos4 2x + 1 – 8 cos2 x = RHS Thus proved.

Step-by-step explanation:

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