Find an algebraic expression that is equivalent to the expression. $\cos ( \arcsin 2 x )$ .
A)$\frac { 1 } { \sqrt { 1 + 4 x ^ { 2 } } }$
B) $\sqrt { 4 x ^ { 2 } - 1 }$
C) $\frac { 1 } { \sqrt { 1 - 4 x ^ { 2 } } }$
D) $\sqrt { 1 - 4 x ^ { 2 } }$
E) $\sqrt { 1 + 4 x ^ { 2 } }$

Question

Find an algebraic expression that is equivalent to the expression. $\cos ( \arcsin 2 x )$ . 
A)$\frac { 1 } { \sqrt { 1 + 4 x ^ { 2 } } }$
B) $\sqrt { 4 x ^ { 2 } - 1 }$
C) $\frac { 1 } { \sqrt { 1 - 4 x ^ { 2 } } }$
D) $\sqrt { 1 - 4 x ^ { 2 } }$
E) $\sqrt { 1 + 4 x ^ { 2 } }$

Quizplus · Accepted Answer

To find an expression equivalent to $\cos ( \arcsin 2x )$, we use the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$. If $\sin \theta = 2x$, then $\cos^2 \theta = 1 - \sin^2 \theta = 1 - (2x)^2 = 1 - 4x^2$. Therefore, $\cos \theta = \sqrt{1 - 4x^2}$, making option D correct.

Find an Algebraic Expression That Is Equivalent to the Expression cos⁡(arcsin⁡2x)\cos ( \arcsin 2 x )cos(arcsin2x)

Find an Algebraic Expression That Is Equivalent to the Expression $\cos ( \arcsin 2 x )$