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}