Question

Answer each of the following.Consider the expression $\tan \left(\frac{\pi}{2}+x\right)$ (a) Why can't we use the identity for $\tan (A+B)$ to express it as a function of $x$ alone? (b) Use the identity $\tan \theta=\frac{\sin \theta}{\cos \theta}$ to rewrite the expression in terms of sine and cosine. (c) Use the result of part (b) to show that $$ \tan \left(\frac{\pi}{2}+x\right)=-\cot x $$

          Answer each of the following.Consider the expression $\tan \left(\frac{\pi}{2}+x\right)$
(a) Why can't we use the identity for $\tan (A+B)$ to express it as a function of $x$ alone?
(b) Use the identity $\tan \theta=\frac{\sin \theta}{\cos \theta}$ to rewrite the expression in terms of sine and cosine.
(c) Use the result of part (b) to show that
$$
\tan \left(\frac{\pi}{2}+x\right)=-\cot x
$$

Added by Dave T.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Darshan Maheshwari

03/18/2022

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Answer each of the following.Consider the expression $\tan \left(\frac{\pi}{2}+x\right)$ (a) Why can't we use the identity for $\tan (A+B)$ to express it as a function of $x$ alone? (b) Use the identity $\tan \theta=\frac{\sin \theta}{\cos \theta}$ to rewrite the expression in terms of sine and cosine. (c) Use the result of part (b) to show that $$ \tan \left(\frac{\pi}{2}+x\right)=-\cot x $$