If cos 4x=1+k sin

Question:

If $\cos 4 x=1+k \sin ^{2} x \cos ^{2} x$, then write the value of $k$.

Solution:

We have,

$\cos 4 x=1+k \sin ^{2} \mathrm{x} \cos ^{2} x$

$\Rightarrow \cos (2 \times 2 x)=1+k \sin ^{2} x \cos ^{2} x$

$\Rightarrow 1-2 \sin ^{2} 2 x=1+k \sin ^{2} x \cos ^{2} x$

$\Rightarrow 1-2(2 \sin x \cos x)^{2}=1+k \sin ^{2} x \cos ^{2} x$

$\Rightarrow 1-8 \sin ^{2} x \cos ^{2} x=1+k \sin ^{2} x \cos ^{2} x$

$\Rightarrow \sin ^{2} x \cos ^{2} x(k+8)=0$

$\Rightarrow k+8=0$

$\therefore k=-8$

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now