Question

$tgx=cos^{2}3+cos ^{2}1-cos4*cos2$

Answer 1

$tgx=cos^23+cos^21-cos4\cdot cos2\\\\\\cos^23+cos^21-cos4\cdot cos2=\\\\=\frac{1+cos6}{2}+\frac{1+cos2}{2}-\frac{1}{2}\cdot (cos(4+2)+cos(4-2))=\\\\=\frac{1}{2}+\frac{cos6}{2}+\frac{1}{2}+\frac{cos2}{2}-\frac{cos6}{2}-\frac{cos2}{2}=1\\\\\\tgx=1\\\\x=\frac{\pi}{4}+\pi n,\; n\in Z$

$Formyla:\; \; \; \; cos^2a= \frac{1+cos2a}{2}\; \; ,\; \; (\; sin^2a=\frac{1-cos2a}{2}\; ) \; .$