Question

$\frac{3\cos \theta +\cos 3\theta }{3\sin \theta -\sin 3\theta }$ is equal to

• A. $1+{\cot }^2\theta$
• B. ${\cot }^4\theta$
• C. ${\cot }^3\theta$
• D. $2\cot \theta$

Answer 1

Answer: (C)

$\frac{3\cos \theta +4{\cos }^3\theta -3\cos \theta }{3\sin \theta -\left(3\sin \theta -4{\sin }^3\theta \right)}=\frac{4{\cos }^3\theta }{4{\sin }^3\theta }={\cot }^3\theta$