Mathematics

Problem

For

0<\alpha<\dfrac{\pi}{2}

, suppose

\sin 2\alpha = \dfrac{12}{13}

. Find the value of

\sin^{4}\alpha + \cos^{4}\alpha

. a)

\dfrac{25}{169}

\dfrac{144}{169}

\dfrac{97}{169}

\dfrac{72}{169}