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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)?

Options

A) 63/65

B) 23/11

C) 61/67

D) 5/13

E) 12/13

The correct answer is A.

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, \(\frac{4}{5} \times \frac{12}{13} + \frac{3}{5} \times \frac{5}{13} = \frac{63}{65}\)

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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, \(\frac{4}{5} \times \frac{12}{13} + \frac{3}{5} \times \frac{5}{13} = \frac{63}{65}\)

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