Convert the expression. $$1 + \cos 4 y$$
A) $2 \cos ^ { 2 } 2 y$
B) $\cos ^ { 2 } 4 y$
C) $\cos ^ { 2 } 2 y$
D) $4 \cos ^ { 2 } 4 y$
E) $2 \cos ^ { 2 } 4 y$

Question

Convert the expression. ​​ $$1 + \cos 4 y$$ ​
A) $2 \cos ^ { 2 } 2 y$
B)​ $\cos ^ { 2 } 4 y$
C)​ $\cos ^ { 2 } 2 y$
D)​ $4 \cos ^ { 2 } 4 y$
E)​ $2 \cos ^ { 2 } 4 y$

Quizplus · Accepted Answer

The expression $1 + \cos 4y$ can be rewritten using the double angle identity for cosine, which states that $\cos 2\theta = 2\cos^2\theta - 1$. Rearranging this formula to solve for $1$ gives $1 = 2\cos^2\theta - \cos 2\theta$. Applying this identity to the given expression with $\theta = 2y$, we get $1 + \cos 4y = 2\cos^2 2y$, which matches option A.

Convert the Expression 1+cos⁡4y1 + \cos 4 y1+cos4y ​ A) 2cos⁡22y2 \cos ^ { 2 } 2 y2cos22y

Convert the Expression $1 + \cos 4 y$
A) $2 \cos ^ { 2 } 2 y$