If \tan(3A)=\cot(A-22^{\circ}), where 3A is an acute angle, then what is the value of A?

Explanation

We use the complementary angle property: \cot(\theta) = \tan(90^{\circ} - \theta). So, \tan(3A) = \tan(90^{\circ} - (A - 22^{\circ})). Equating the angles, we get 3A = 90^{\circ} - A + 22^{\circ}. Solving this yields 4A = 112^{\circ}, which simplifies to A = 28^{\circ}.

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...