Write an algebraic expression that is equivalent to $\tan ( \arccos 3 x )$.
A) $\frac { 1 } { 3 x }$
B) $\frac { \sqrt { 1 - 9 x ^ { 2 } } } { 3 x }$
C) $\sqrt { 1 - 9 x ^ { 2 } }$
D) $\frac { 1 } { \sqrt { 1 - 9 x ^ { 2 } } }$
E) $3 x$

Question

Quizplus · Accepted Answer

To find an expression equivalent to $\tan ( \arccos 3 x )$, we use the trigonometric identity $\tan(\theta) = \frac{\sqrt{1 - \cos^2(\theta)}}{\cos(\theta)}$. Here, $\theta = \arccos(3x)$, so $\cos(\theta) = 3x$. Plugging this into the identity gives $\tan ( \arccos 3 x ) = \frac{\sqrt{1 - (3x)^2}}{3x} = \frac{\sqrt{1 - 9x^2}}{3x}$.

Write an Algebraic Expression That Is Equivalent To tan⁡(arccos⁡3x)\tan ( \arccos 3 x )tan(arccos3x)

Write an Algebraic Expression That Is Equivalent To $\tan ( \arccos 3 x )$