What is the value of \sin 24^{\circ}\sin 66^{\circ}-\cos 24^{\circ}\cos 66^{\circ}+\tan 24^{\circ}\tan 66^{\circ}-\cot 24^{\circ}\cot 66^{\circ}?

Explanation

Since 66^{\circ} = 90^{\circ} - 24^{\circ}, we have \sin 66^{\circ} = \cos 24^{\circ} and \tan 66^{\circ} = \cot 24^{\circ}. Thus, \sin 24^{\circ}\cos 24^{\circ} - \cos 24^{\circ}\sin 24^{\circ} + \tan 24^{\circ}\cot 24^{\circ} - \cot 24^{\circ}\tan 24^{\circ} = 0 + 1 - 1 = 0.

Related questions on Trigonometry

• Two poles are situated 24 m apart and their heights differ by 10 m. What is the distance between their tips?
• If \frac{\cos \theta}{1 - \sin \theta} + \frac{\cos \theta}{1 + \sin \theta} = 4, then which one of the following is a value of $(\tan^2 \...
• For 0 < \theta < \frac{\pi}{2}, consider the following : I. $(\tan^4 \theta + \tan^6 \theta)(\cot^4 \theta + \cot^6 \theta) = \sec^2 \the...
• If 3\sin \theta + 4\cos \theta = 5, then what is a value of 4\tan \theta + 3\cot \theta ?
• At a point on level ground, the tangent of the angle of elevation of the top of a tower is found to be \frac{5}{6}. On walking 70 m toward...