Question

If $\alpha$ and $\beta$ are complementary angle such that qsin$\alpha$ = P , then find the value of $(\sin \alpha \cos \beta -\cos \alpha \sin \beta )$

Answer 1

$\alpha ,\beta$ are complimentary angles.

$\alpha +\beta =90$

$\sin \alpha =\frac{p}{q}=\cos \beta$

$\cos \alpha =\frac{\sqrt{q^2-p^2}}{q}=\sin \beta$

$(\sin \alpha \cos \beta -\cos \alpha \sin \beta )=(\frac{p^2}{q^2}-\frac{q^2-p^2}{q^2})$

$=2\left(\frac{p^2}{q^2}\right)-1$