If $f(x)=\sin^2 x+\sin ^2\left(x+\frac{\pi}{3}\right)+\cos x \cos \left(x+\frac{\pi}{3}\right)$ and $g\left(\frac{5}{4}\right)=1$, then (gof) (x) is equal to

1

$\sin^2 x+\sin ^2\left(x+\frac{\pi}{3}\right)+\cos x \cos \left(x+\frac{\pi}{3}\right)$

$⇒\sin^2 x+\left(\sin x\cos\frac{\pi}{3}+\cos x\sin\frac{\pi}{3}\right)^2+\cos x\left(\cos x\cos\frac{\pi}{3}-\sin x\sin\frac{\pi}{3}\right)$

$=\sin^2x+\frac{\sin^2x}{4}+\frac{3}{4}\cos^2x+\frac{2\sqrt{3}}{4}\sin x\cos x+\frac{\cos^2x}{2}-\frac{\sqrt{3}}{2}\cos x\sin x$

$=\frac{5}{4}(\sin^2x+\cos^2x)=\frac{5}{4}=f(x)⇒gof(x)=1$