Use a double angle formula to rewrite the given expression. $10 \cos ^ { 2 } x - 5$
A) $5 \cos 5 x$
B) $5 \cos 2 x$
C) $10 \cos 2 x$
D) $2 \cos 10 x$
E) $2 \cos 5 x$

Question

Use a double angle formula to rewrite the given expression. $10 \cos ^ { 2 } x - 5$
A) $5 \cos 5 x$
B) $5 \cos 2 x$  
C) $10 \cos 2 x$  
D) $2 \cos 10 x$  
E) $2 \cos 5 x$

Quizplus · Accepted Answer

The double angle formula for cosine is $\cos(2x) = 2\cos^2(x) - 1$. Rearranging the given expression $10\cos^2(x) - 5$ as $5(2\cos^2(x) - 1)$, we can see it matches the form $5\cos(2x)$, making option B correct.

Use a Double Angle Formula to Rewrite the Given Expression 10cos⁡2x−510 \cos ^ { 2 } x - 510cos2x−5

Use a Double Angle Formula to Rewrite the Given Expression $10 \cos ^ { 2 } x - 5$