What is the value of the following? \frac{2 \sin 68^\circ}{\cos 22^\circ} - \frac{2 \cot 15^\circ}{5 \tan 75^\circ} - \frac{3 \tan 20^\circ \tan 40^\circ \tan 45^\circ \tan 50^\circ \tan 70^\circ}{5}

Explanation

Using complementary angles \sin(90^\circ-\theta) = \cos \theta and \tan(90^\circ-\theta) = \cot \theta: \frac{2\cos 22^\circ}{\cos 22^\circ} - \frac{2\tan 75^\circ}{5\tan 75^\circ} - \frac{3 \times 1 \times 1 \times 1}{5} = 2 - \frac{2}{5} - \frac{3}{5} = 2 - 1 = 1.

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...