If π2<α<π,π<β<3π2;sin⁡α=1517 and tan⁡β=125 then the value of sin⁡(β−α) is

If π2

A
$- \frac{171}{221}$
B
$- \frac{21}{221}$
C
$\frac{21}{221}$
D
$\frac{171}{221}$

Solution:

Given,

$\begin{array}{l} \sin α = \frac{15}{17}, \tan β = \frac{12}{5} \\ ∴ since \frac{π}{2} < α < π, π < β < \frac{3 π}{2} \\ \cos α = - \frac{8}{17}, \sin β = - \frac{12}{13} \\ and \cos β = - \frac{5}{13} \end{array}$

Now,

$\begin{matrix} \sin (β - α) = \sin βcos α - \cos βsin α \\ = - \frac{12}{13} (\frac{- 8}{17}) - (\frac{- 5}{13}) (\frac{15}{17}) \\ = \frac{96}{221} + \frac{75}{221} \\ = \frac{171}{221} \end{matrix}$

If $\frac{π}{2} < α < π, π < β < \frac{3 π}{2}; \sin α = \frac{15}{17}$ and $\tan β = \frac{12}{5}$ then the value of $\sin (β - α)$ is

Solution:

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