Find the value of $\sin ^4 30^{\circ}+\cos ^4 30^{\circ}-\sin 25^{\circ} \cos 65^{\circ}-\sin 65^{\circ} \cos 25^{\circ}$.
Answer & explanation
Correct answer: option 1
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
= - \(\frac{6}{16}\)
= - \(\frac{3}{8}\)