Question

If $\sin A=\frac{1}{2}$ and $\cos B=\frac{\sqrt{3}}{2}$ where A lies in second quadrant and B lies in first quadrant, find the values of (a) $\sin (A-B)\left(b\right)\cos (A-B)\left(c\right)\tan (A+B)$

Answer 1

$\sin A=\frac{1}{2}A\to II$ Quad

So, $f={150}^o(\because \sin (180-\theta )=\sin \theta )$

$\cos B=\frac{\sqrt{3}}{2}B\to I$ Quad

So, $B={30}^o$

$a\left)\sin \right(A-B)=\sin ({120}^o)$

$=\sin (90+{30}^o)$

$=\cos {30}^o$

$=\frac{\sqrt{3}}{2}$

$b\left)\cos \right(A-B)=\cos ({120}^o)$

$=\cos (90+{30}^o)$

$=-\sin {30}^o$

$=\frac{\sqrt{-1}}{2}$

$c\left)\tan \right(A+B)=\tan ({180}^o)$

$=0$