Krishna
0

Step 1: Note down the given data and recall the double angle identities

\sin x = \frac{\sqrt{2}}{4}

\cos x = ?

Double identities:

\cos 2\theta = \cos^2 \theta - \sin^2\theta

\cos 2\theta = 2 \cos^2 - 1 \theta

\cos 2 \theta = 1 - 2\sin^2\theta

Step 2: Choose the appropriate formula to calculate \cos 2x

We know the \sin \theta so take

\cos 2x = 1 - 2\sin^2 x

\cos 2x = 1 - 2(\frac{\sqrt{2}}{4})^2   \because \sin x = \frac{\sqrt{2}}{4}

\cos 2x = 1 - 2(\frac{2}{16})

\cos 2x = 1 - \frac{1}{4}

\cos 2x = \frac{3}{4}