Which of these is an identity?

(A) $\cot u = - \sin \frac{u}{\cos} u$ (B) $\sec u = - \sin \left(\frac{1}{u}\right)$ (C) $\cot u = \frac{1}{\tan} u$ (D) ${\tan}^{2} u + {\cot}^{2} u = 1$

Jan 19, 2017

(C) $\cot u = \frac{1}{\tan} u$ is the only identity

Explanation:

(A) $\cot u = - \sin \frac{u}{\cos} u$ is not an identity as $\cot u = \cos \frac{u}{\sin} u$ and not $- \sin \frac{u}{\cos} u$.

(B) $\sec u = - \sin \left(\frac{1}{u}\right)$ too is not an identity as $\sec u = \frac{1}{\cos} u$

(D) ${\tan}^{2} u + {\cot}^{2} u = 1$ is not an identity as ${\tan}^{2} u = \frac{1}{\cot} ^ 2 u$

(C) $\cot u = \frac{1}{\tan} u$ is the only identity