Use a double-angle formula to rewrite the expression.
$6 \sin ^ { 2 } x - 3$
A) $- 3 \cos 2 x$
B) $3 \cos 2 x$
C) $- 6 \cos x$
D) $3 \cos x$
E) $6 \cos 2 x$

Question

Use a double-angle formula to rewrite the expression. 
$6 \sin ^ { 2 } x - 3$ 
A) $- 3 \cos 2 x$
B) $3 \cos 2 x$
C) $- 6 \cos x$
D) $3 \cos x$
E) $6 \cos 2 x$

Quizplus · Accepted Answer

The expression $6 \sin ^ { 2 } x - 3$ can be rewritten using the double-angle formula for cosine, which is $\cos 2x = 1 - 2\sin^2x$. Rearranging this formula gives $2\sin^2x = 1 - \cos 2x$, and multiplying both sides by 3 gives $6\sin^2x = 3 - 3\cos 2x$. Therefore, $6 \sin ^ { 2 } x - 3 = - 3 \cos 2 x$.

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Use a Double-Angle Formula to Rewrite the Expression $6 \sin ^ { 2 } x - 3$