What is \tan \theta + \cot \theta equal to?
For the following two (02) items: Let \sin \theta + \cos \theta = p and \sec \theta + \operatorname{cosec} \theta = q, where p \neq 1.
- A. p/q
- B. q/p ✓
- C. 2p/q
- D. 2q/p
Correct Answer: B. q/p
Explanation
\tan \theta + \cot \theta = \frac{\sin^2 \theta + \cos^2 \theta}{\sin \theta \cos \theta} = \frac{1}{\sin \theta \cos \theta}. From the previous equations, q = \frac{p}{\sin \theta \cos \theta}, so \frac{1}{\sin \theta \cos \theta} = \frac{q}{p}.
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...