Question

25^2cos(x+3pi/2)=(1/5)^2cos(x+pi)

Answer 1

$25^{2cos(\frac{3\pi}{2}+x)}=(\frac{1}{5})^{2cos(\pi+x)}\\(5^2)^{2cos(\frac{3\pi}{2}+x)}=(5^2)^{-cos(\pi+x)}\\2cos(\frac{3\pi}{2}+x)+cos(\pi+x)=0\\2sinx-cosx=0\\2sinx=cosx|:cosx\\2tgx=1\\tgx=\frac{1}{2}\to x=arctg\frac{1}{2}+\pi n,n\in Z$