Trigo-equation

**SADANE ANTAR** · December 12th 2009, 05:44 AM

Solve in R :
$<br /> 4(\cos ^{4}(x)+\sin ^{4}(x))=7\cos (2x+\frac{\pi }{6})\cos (2x-\frac{\pi }{6})<br />$

**mathaddict** · December 12th 2009, 06:16 AM

Originally Posted by SADANE ANTAR

Solve in R :
$<br /> 4(\cos ^{4}(x)+\sin ^{4}(x))=7\cos (2x+\frac{\pi }{6})\cos (2x-\frac{\pi }{6})<br />$

HI

$4(\cos^4 x+\sin^4 x)=7\cos (2x+30)\cos (2x-30)$

$4[(\cos^2 x+\sin^2 x)^2-\frac{1}{2}(4\cos^2 x\sin^2 x)]=$ [tex]7{\frac{1}{2}[\cos (2x+30+2x-30)+\cos (2x+30-2x+30)]}[\MATH]

$4(1-\frac{1}{2}\sin^2 2x)=\frac{7}{2}(\cos 4x+\frac{1}{2})$

$4-2\sin^2 2x =\frac{7}{2}[\cos 2(2x)+\frac{1}{2}]$

$8-4\sin^2 2x=7(1-2\sin^2 2x+\frac{1}{2})$

$16-8\sin^2 2x=21-14\sin^2 2x$

Solve $\sin 2x=\sqrt{\frac{5}{6}}$

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