If $\sin\beta$ is the G.M. between $\sin\alpha$ and $\cos\alpha$, then $\cos2\beta$ is equal to
🎥 Video solution / Text Solution of this question is given below:
Since $\sin\beta$ is the G.M. of $\sin\alpha$ and $\cos\alpha$,
$\sin^2\beta=\sin\alpha\cos\alpha=\dfrac12\sin2\alpha$
So,
$\cos2\beta=1-2\sin^2\beta=1-\sin2\alpha$
But
$1-\sin2\alpha=2\sin^2\left(\dfrac{\pi}{4}-\alpha\right)$