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(a) If $\sec A = \frac{25}{7}$, then find the value of $\text{cosec } A$ and $\tan A$.
OR
(b) Verify that $\sin (A + B) = \sin A \cos B + \cos A \sin B$ for $A = 60^\circ$ and $B = 30^\circ$.
OR
(b) Verify that $\sin (A + B) = \sin A \cos B + \cos A \sin B$ for $A = 60^\circ$ and $B = 30^\circ$.
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Solution: (a) $\text{cosec } A = \frac{25}{24}$ and $\tan A = \frac{24}{7}$
OR
(b) $LHS = \sin (60^\circ + 30^\circ) = \sin 90^\circ = 1$
$RHS = \sin 60^\circ \cos 30^\circ + \cos 60^\circ \sin 30^\circ = \frac{\sqrt{3}}{2} \times \frac{\sqrt{3}}{2} + \frac{1}{2} \times \frac{1}{2} = 1 = LHS$
OR
(b) $LHS = \sin (60^\circ + 30^\circ) = \sin 90^\circ = 1$
$RHS = \sin 60^\circ \cos 30^\circ + \cos 60^\circ \sin 30^\circ = \frac{\sqrt{3}}{2} \times \frac{\sqrt{3}}{2} + \frac{1}{2} \times \frac{1}{2} = 1 = LHS$