Chapter 12

\(8 \sin ^{6} x+3 \cos 2 x+2 \cos 4 x+1=0\)

\(3(1-\sin x)=1+\cos 2 x\)

\(\sin x=\frac{3}{4} \cos x\)

\(3 \sin x=2 \cos x\)

\(3 \sin ^{2} x+3 \sin x \cos x-6 \cos ^{2} x=0\)

\(\sin ^{2} x+3 \cos ^{2} x-2 \sin 2 x=0\)

\(3 \sin ^{2} x+2 \sin x \cos x=2\)

\(2 \cos ^{2} x-3 \sin x \cos x+5 \sin ^{2} x=3\)

\(\cos ^{2} x+\sin x+1=0\)

\(\tan 2 x \tan x=1\)

\((\sqrt{3}-1) \sin x+(\sqrt{3}+1) \cos x=2\)

\(\sin 7 x=\sin 4 x-\sin x\)

\(\sin 2 x=\cos 3 x\)

\(4 \sin x \cos x-2 \cos x-2 \sqrt{3} \sin x+\sqrt{3}=0\)

\(\tan 3 x=\tan 5 x\)

\(\sin 5 x \cos 3 x=\sin 9 x \cos 7 x\)

\(\sin 6 x \cos 2 x=\sin 5 x \cos 3 x-\sin 2 x\)

\(\sin ^{6} x+\cos ^{6} x=\frac{7}{16}\)

\(2 \cos ^{2} x+\cos 5 x=1\)

\(\sin x+\sin 2 x+\sin 3 x=0\)

\(\sin x+\sin 3 x+\cos x+\cos 3 x=0\)

\(\sin x+\cos x=1\)

$$ \cos x+\sqrt{3} \sin x=2 $$

$$ \sqrt{3} \sin 2 x+\cos 2 x=\sqrt{2} $$

$$ \frac{1}{2} \sin 3 x+\frac{\sqrt{3}}{2} \cos 3 x=\sin 5 x $$

$$ 2 \cos 3 x+\sqrt{3} \sin x+\cos x=0 $$

$$ \sin 5 x+\cos 5 x=\sqrt{2} \cos 13 x $$

$$ \sin ^{2} x-\cos 2 x=2-\sin 2 x $$

$$ \sin ^{2} x \cos ^{2} x-10 \sin x \cos ^{3} x+21 \cos ^{4} x=0 $$

$$ 8 \sin ^{2} \frac{x}{2}-3 \sin x-4=0 $$

$$ \sin ^{4} x+\cos ^{4} x=\cos 4 x $$

$$ \cos ^{4} x+\sin ^{4} x-\sin 2 x+\frac{3}{4} \sin ^{2} 2 x=0 $$

$$ 3 \tan \frac{x}{2}+\cot x=\frac{5}{\sin x} $$

$$ \cos 2 x-3 \cos x+1=\frac{1}{(\cot 2 x-\cot x) \sin (x-\pi)} $$

$$ \cos x=\frac{\tan x}{1+\tan ^{2} x} $$

$$ \cot x+\frac{\sin x}{1+\cos x}=2 $$

$$ 2 \sin x-3 \cos x=3 $$

$$ 3 \sin 2 x+\cos 2 x=2 $$

$$ \cos 4 x+2 \sin 4 x=1 $$

$$ \sin 2 x+\tan x=2 $$

$$ \frac{1+\sin x}{1+\cos x}=\frac{1}{2} $$

$$ \sin ^{3} x+\cos ^{3} x=1 $$

$$ 4 \sin ^{4} 3 x-3 \cos x+5=0 $$

$$ \sin x \cos x-6 \sin x+6 \cos x+6=0 $$

$$ 4-4(\cos x-\sin x)-\sin 2 x=0 $$

$$ 5 \sin 2 x-11(\sin x+\cos x)+7=0 $$

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

$$ \cos x \cos 2 x \cos 4 x \cos 8 x=\frac{1}{16} $$

$$ 2 \sin 17 x+\sqrt{3} \cos 5 x+\sin 5 x=0 $$

$$ 4 \cos ^{3} \frac{x}{2}+3 \sqrt{2} \sin x=8 \cos \frac{x}{2} $$