If 4x=1+K ^2x ^2, then write the value of k. - Vidyadip

Question

If $\cos4\text{x}=1+\text{K}\sin^2\text{x}\cos^2\text{},$ then write the value of k.

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Answer

We have,
$\cos4\text{x}=1+\text{k}\sin^2\text{x}\cos^2\text{x}\ .....(\text{i})$
$\Rightarrow\cos2.2\text{x}-\cos^22\text{x}-\sin^2\text{x}$
$=1-2\sin^22\text{x}$
$=1-2(2\sin\text{x}\cos\text{x})^2$
$=1-8\sin^2\text{x}\cos^2\text{x}\ .....(\text{ii})$
compaiing (i) & (ii), we get
$\text{k}=-8$

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