Practicing Success
Find the value of $\sin ^4 30^{\circ}+\cos ^4 30^{\circ}-\sin 25^{\circ} \cos 65^{\circ}-\sin 65^{\circ} \cos 25^{\circ}$. |
$-\frac{3}{8}$ 0 $\frac{5}{8}$ $\frac{13}{8}$ |
$-\frac{3}{8}$ |
sin4 30º + cos4 30º - sin25º.cos65º - sin65º.cos25º { using , sin ( A + B ) = sinA.cosB + cosA.sinB } = (\(\frac{1}{2}\))4 + (\(\frac{√3}{2}\))4 - sin ( 25º + 65º ) = \(\frac{1}{16}\) + \(\frac{9}{16}\) - 1 = \(\frac{10}{16}\) - 1 = - \(\frac{6}{16}\) = - \(\frac{3}{8}\) |