Question

Solve: $\frac{\sin 3\theta +\cos 3\theta }{\cos \theta -\sin \theta }$

Answer 1

$=\frac{sin30+cos30}{cos\theta -sin\theta }=\frac{3sin\theta -4si{n}^3\theta +4co{s}^3\theta -3cos\theta }{cos\theta -sin\theta }$

$=\frac{4(co{s}^3\theta -si{n}^3\theta )+3(sin\theta -cos\theta )}{cos\theta -sin\theta }$

$=\frac{4(cos\theta -sin\theta )(co{s}^2\theta +cos\theta sin\theta +si{n}^2\theta )-3(cos\theta -sin\theta )}{cos\theta -sin\theta }$

$=\frac{(cos\theta -sin\theta )4(1+cos\theta sin\theta -3)}{cos\theta -sin\theta }$

$=4(1+cos\theta sin\theta )-3$

$=4+4cos\theta sin\theta -3$

$=1+2.2cos\theta sin\theta$

$=1+2sin20\theta$