Given that $\tan A = -\frac{5}{12}$, $\cos B = \frac{3}{5}$ and that $A$ and $B$ a

Question

Given that $\tan A = -\frac{5}{12}$, $\cos B = \frac{3}{5}$ and that $A$ and $B$ are in the same quadrant, for $0^\circ < A < 360^\circ$, $0^\circ < B < 360^\circ$, calculate without using a calculator, the value of each of the following. $\sin (A - B)$ $\cos (2A + B)$ $\sin \frac{1}{2} A$ $\tan (A + B)$ $\cot (A + 2B)$ $\cos \frac{1}{2} A$

Accepted Answer

(i) $\dfrac{33}{65}$; (ii) $-\dfrac{63}{16}$; (iii) $-\dfrac{123}{845}$; (iv) $\dfrac{204}{253}$; (v) $\dfrac{\sqrt{26}}{26}$; (vi) $-\dfrac{5\sqrt{26}}{26}$

Trigonometry - Compound and Double-Angle Identities

Trigonometry - Compound and Double-Angle Identities

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