Prove that: 4x=1-8 ^2x+8 ^4x - Vidyadip

Question

Prove that: $\cos4\text{x}=1-8\cos^2\text{x}+8\cos^4\text{x}$

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Answer

$\text{LHS}=\cos4\text{x}$ $=\cos2.2\text{x}$ $=2\cos^22\text{x}=1$ $[\because\cos2\theta=1\cos^2\theta-1]$ $=2(2\cos2\text{x}-1)^2-1$ $=2(4\cos^4\text{x}-4\cos^2\text{x}+1)-1$ $8\cos^4\text{x}-8\cos^4\text{x}+1$ $=1=8\cos^2\text{x}+8\cos^4\text{x}=\text{RHS}$

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