If sin theta+cos theta=frac{1}{2}, then 16(si | vedclass

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Question

$16[2 \sin 4 	heta \cos 2 	heta+\cos 4 	heta]$

$16\left[4 \sin 2 	heta \cos ^{2} 2 	heta+2 \cos ^{2} 2 	heta-1ight]$

Now:

$\sin 	het

Vedclass · Accepted Answer

$-23$

Vedclass · Answer

$16[2 \sin 4 	heta \cos 2 	heta+\cos 4 	heta]$

$16\left[4 \sin 2 	heta \cos ^{2} 2 	heta+2 \cos ^{2} 2 	heta-1ight]$

Now:

$\sin 	heta+\cos 	heta=\frac{1}{2}$

$1+\sin 2 	heta=\frac{1}{4}$

$\sin 2 	heta=-\frac{3}{4}$

$\cos ^{2} 2 	heta=1-\frac{9}{16}=\frac{7}{16}$

$16\left[-4(-3 / 4) 	imes \frac{7}{16}+2 	imes \frac{7}{16}-1ight]$

$16\left[\frac{-7}{16}-1ight] \Rightarrow-23$

If $\sin \theta+\cos \theta=\frac{1}{2}$, then $16(\sin (2 \theta)+\cos (4 \theta)+\sin (6 \theta))$ is equal to:

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