Question

If $2si{n}^2((\pi /2)co{s}^{2}x)=1-cos(\pi sin2x),x\ne (2n+1)\pi /2,n\in I$, then $cos2x$ is equal to _____ .

Answer 1

Answer: 0.6

The given equation is equivalent to
$2si{n}^2((\pi /2)co{s}^{2}x)=2si{n}^2((\pi /2)sin2x)$
or $co{s}^{2}x=sin2x$
or $cosx(cosx-2sinx)=0$
$\Rightarrow 1-2tanx=0$ as $cosx\ne 0,x\ne (2n+1)\frac{\pi }{2}$
or $tanx=\frac{1}{2}$
$\Rightarrow cos2x=\frac{1-ta{n}^{2}x}{1+ta{n}^{2}x}=\frac{3}{5}$