Exams › SSC CGL (Prelims) › General

If \(\cos A = \frac{4}{5}\) and \(\sin B = \frac{5}{13}\), with \(A,B \in (0,\pi/2)\), find \(\cos(A-B)\).

1. \(\frac{33}{65}\)
2. \(\frac{48}{65}\)
3. \(\frac{56}{65}\)
4. \(\frac{63}{65}\)

Correct answer: \(\frac{63}{65}\)

Solution

Since \(A\) and \(B\) are acute, all trigonometric ratios are positive. We get \(\sin A=3/5\) and \(\cos B=12/13\), so \(\cos(A-B)=\frac{4}{5}\cdot\frac{12}{13}+\frac{3}{5}\cdot\frac{5}{13}=\frac{63}{65}\).

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