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  4. The value of ( sin 24° cos 6°- sin 6° sin 66°/ sin 21° cos 39°- cos 51° sin 69°) is

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Q. The value of $\frac{\sin 24^{\circ} \cos 6^{\circ}-\sin 6^{\circ} \sin 66^{\circ}}{\sin 21^{\circ} \cos 39^{\circ}-\cos 51^{\circ} \sin 69^{\circ}}$ is

Trigonometric Functions

Solution:

$\frac{\sin 24^{\circ} \cos 6^{\circ}-\sin 6^{\circ} \cos 24^{\circ}}{\sin 21^{\circ} \cos 39^{\circ}-\sin 39^{\circ} \cos 21^{\circ}}=\frac{\sin \left(24^{\circ}-6^{\circ}\right)}{\sin \left(21^{\circ}-39^{\circ}\right)}$
$=\frac{\sin 18^{\circ}}{\sin \left(-18^{\circ}\right)}=-1$