If$\ \ \frac{\pi}{2}

Question

If$\ \ \frac{\pi}{2} < \alpha < \pi,\pi < \beta < \frac{3\pi}{2};\sin{\alpha = \frac{15}{17}\ and	an{\beta = \frac{12}{5},\ }}$ then the value of $\sin{(\beta - \alpha)}$ is

Dr. Abubacker · Accepted Answer

(d)
Given, $\sin{\alpha = \frac{15}{17},	an{\beta = \frac{12}{5}}}$
Since$,\ \frac{\pi}{2} < \alpha < \pi,\ \pi < \beta < \frac{3\pi}{2}$
$	herefore\cos{\alpha = - \frac{8}{17},\sin{\beta = - \frac{12}{13}}}$
and$\ \cos{\beta = - \frac{5}{13}}$
Now$,\sin{(\beta - \alpha) = \sin{\beta\cos{\alpha - \cos{\beta\sin\alpha\ }}}}$
$= - \frac{12}{13}\left( \frac{- 8}{17} ight) - \left( \frac{- 5}{13} ight)\left( \frac{15}{17} ight)$
$= \frac{96}{221} + \frac{75}{221} = \frac{171}{221}$

Q. If$\ \ \frac{\pi}{2} < \alpha < \pi,\pi < \beta < \frac{3\pi}{2};\sin{\alpha = \frac{15}{17}\ and\tan{\beta = \frac{12}{5},\ }}$ then the value of $\sin{(\beta - \alpha)}$ is

Explanation

Reviewed by Dr. Abubacker

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