Question:
sin 38° – cos 52° = ?
(a) 0
(b) 1
(c) $\frac{\sqrt{3}}{2}$
(d) $\frac{2}{\sqrt{3}}$
Solution:
$\sin 38^{\circ}-\cos 52^{\circ}$
$=\sin \left(90^{\circ}-52^{\circ}\right)-\cos 52^{\circ}$
$=\cos 52^{\circ}-\cos 52^{\circ} \quad\left(\because \sin \left(90^{\circ}-\theta\right)=\cos \theta\right)$
$=0$
Hence, the correct option is (a).
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