Question

$\sin {420}^o\cos {330}^o+\cos (-{300}^o)\sin {150}^o=?$

Answer 1

$\sin {420}^o\cos {330}^o+\cos (-{300}^o)\sin {150}^o$

$\Rightarrow \sin ({360}^o+{60}^o)\cos ({360}^o+{30}^o)+\cos {300}^o\sin {150}^o$

$\Rightarrow \sin {60}^o\cos {30}^o+\cos ({360}^o-{60}^o)\sin ({180}^o-{30}^o)$

$\Rightarrow \sin {60}^o\cos {30}^o+\cos {60}^o\sin {30}^o$

$\Rightarrow \sin ({60}^o+{30}^o)$

$\Rightarrow \sin {90}^o=1$

$\left[\begin{array}{c}\cos (-x)=\cos x\\ \sin (2\pi +x)=\sin x\\ \cos (2\pi -x)=\cos x\\ \sin (\pi -x)=\sin x\end{array}\right]$.