Question

cos3x*cos4x-sin3x*sin4x=1/2

Answer 1

$Cos3x*Cos4x-Sin3x*Sin4x=\frac{1}{2}\\\\Cos(3x+4x)=\frac{1}{2}\\\\Cos7x=\frac{1}{2}\\\\7x=\pm arc Cos\frac{1}{2}+2\pi n,n\in Z\\\\7x=\pm \frac{\pi }{3}+2\pi n,n\in Z\\\\x=\pm \frac{\pi }{21} +\frac{2\pi n }{7},n\in Z$