Given that $\cos(A - B) = \frac{4}{5}$, $\sin A \sin B = \frac{1}{10}$ and that $A$

Question

Given that $\cos(A - B) = \frac{4}{5}$, $\sin A \sin B = \frac{1}{10}$ and that $A$ and $B$ are both acute angles, calculate without using a calculator, the value of each of the following. $\cos A \cos B$ $\cos(A + B)$ $\sin\left(\frac{A + B}{2}\right)$ $\tan A \tan B$ $\sin 2A \sin 2B$ $\sec\left(\frac{A + B}{2}\right)$

Accepted Answer

(i) $\dfrac{7}{10}$; (ii) $\dfrac{1}{7}$; (iii) $\dfrac{3}{5}$; (iv) $\dfrac{7}{25}$; (v) $\dfrac{\sqrt{5}}{5}$; (vi) $\dfrac{\sqrt{5}}{2}$

Trigonometry - Compound and Double-Angle Identities

Trigonometry - Compound and Double-Angle Identities

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