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# If Sin A = 4/5 and Cos B = 12/13. find the value of Sin (A + B)?

### Question

If Sin A = 4/5 and Cos B = 12/13. find the value of Sin (A + B)?

A) 63/65

B) 23/11

C) 61/67

D) 5/13

E) 12/13

### Explanation:

$$\sin(A+B)$$
$$\sin A \cos B + \sin B \cos A$$
$$\sin A = \frac{4}{5}$$
$$\cos A = \frac{3}{5}$$
$$\sin B = \frac{5}{13}$$
$$\cos B = \frac{12}{13}$$
Therefore, $$\frac{4}{5} \times \frac{12}{13} + \frac{3}{5} \times \frac{5}{13} = \frac{63}{65}$$

## Dicussion (1)

• $$\sin(A+B)$$
$$\sin A \cos B + \sin B \cos A$$
$$\sin A = \frac{4}{5}$$
$$\cos A = \frac{3}{5}$$
$$\sin B = \frac{5}{13}$$
$$\cos B = \frac{12}{13}$$
Therefore, $$\frac{4}{5} \times \frac{12}{13} + \frac{3}{5} \times \frac{5}{13} = \frac{63}{65}$$