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Given that $sin x = \frac{4}{5}$ and \(cos y = \frac{12}{1...

Given that $sin x = \frac{4}{5}$ and $cos y = \frac{12}{13}$ , where x is an obtuse angle and y is an acute angle, find the value of sin (x - y).

A.

$\frac{63}{65}$

B.

$\frac{48}{65}$

C.

$\frac{56}{65}$

D.

$\frac{16}{65}$

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Correct answer is A

$sin x = \frac{4}{5}$ and $cos y = \frac{12}{13}$

x is obtuse i.e sin x = + ve while cos x = + ve

$cos x=\frac{3}{5}==>cos x=-\frac {3}{5}(obtuse)$

$sin y= \frac{5}{13}$

$sin (x-y) = sin x$ $cos y - cos x$ $sin y$

$sin(x-y) = \frac{4}{5}\times\frac{12}{13}-(-\frac{3}{5})\times\frac{5}{13}$

$sin(x-y) = \frac{48}{65}-(-\frac{3}{13})$

$\therefore sin (x-y) = \frac{48}{65} + \frac{3}{13} = \frac{63}{65}$

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