If sin A = 45 and cos B = - 1213, where A and B lie in first and t

Question -

If sin A = $\frac{4}{5}$ and cos B = - $\frac{12}{13}$ , where A and B lie in first

and third quadrant respectively, then cos(A + B) =

Options:

A .

\frac{56}{65}

B . -

\frac{56}{65}

C .

\frac{16}{65}

D . -

\frac{16}{65}

Answer: Option D
:
D

We have sin A = $\frac{4}{5}$ and cos B = - $\frac{12}{13}$

Now, cos(A + B) = cos A cos B - sin A sin B

= $\sqrt{1 - \frac{16}{25}}$ $(- \frac{12}{13})$ - $\frac{4}{5}$ $(- \sqrt{1 - \frac{144}{169}})$

= - $\frac{3}{5}$ × $\frac{12}{13}$ - $\frac{4}{5}$ $(- \frac{5}{13})$ = - $\frac{16}{65}$

(Since A lies in first quadrant and B lies in third quadrant).

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