Question

Помогите решить пример, пожалуйста

Answer 1

$\displaystyle \frac{(cos( \frac{ \pi }{2}-2a))^2+4(cos( \frac{3 \pi }{2}-a))^2-4}{1+cos(-( \pi -4a))-8(sin( \pi -a))^2}= \\\\= \frac{sin^22a+4sin^2a-4}{1-cos4a-8sin^2a}= \frac{4sin^2a*cos^2a+4sin^2a-4(sin^2a+cos^2a)}{1-(1-2sin^22a)-8sin^2a}=\\\\= \frac{4sin^2a*cos^2a-4cos^2a}{2sin^22a-8sin^2a}= \frac{4cos^2a(sin^2a-1)}{2*4sin^2a*cos^2a-8sin^2a}=\\\\= \frac{4cos^2a(-cos^2a)}{8sin^2a(cos^2a-1)}= \frac{-4cos^4a}{8sin^2a(-sin^2a)}= \frac{-4cos^4a}{-8sin^4a}= \frac{1}{2}ctg^4a$