Question

how under root of {2A^2 x (1+ cos theta)}=under root of {4A^2 x cos^2theta/2} ?

Answer 1

Hey :) Welcome to OpenStudy!

I'm not sure what your question is.
There is no simpler way to express 1+cos(theta).

Answer 2

\(\rm 1+\cos\theta\) is an expression, there is nothing to solve.
Are you trying to solve this?
\(\rm 1+\cos\theta=0\)

Answer 3

\[\cos(2 u)=\cos^2(u)-\sin^2(u) \\ \cos(2 u)=\cos^2(u)-(1-\cos^2(u)) \\ \cos(2 u)=2 \cos^2(u)-1 \\ \text{ solve for } \cos^2(u) \\ \cos^2(u)=\frac{1}{2}(\cos(2 u)+1) \\ \text{ Let } u=\frac{\theta}{2} \\ \cos^2(\frac{\theta}{2})=\frac{1}{2}(\cos(
\theta)+1) \\ \text{ or let's write it as } \\ 2 \cos^2(\frac{\theta}{2})=\cos(\theta)+1 \\ \text{ so you can replace } \cos(\theta)+1 \text{ with } 2\cos^2(\frac{\theta}{2})\]

Answer 4

The identity is called the half angle identity.

Answer 5

\[\sqrt{2 A^2 (1+ \cos(\theta)} = \sqrt{2 A^2 (2 \cos^2(\frac{\theta}{2}))} =\sqrt{4 A^2\cos^2(\frac{\theta}{2})}\]

Answer 6

so both the left and right expressions are equal

Answer 7

thanks freckles

Answer 8

np

Answer 9

was this part of a calculus question you were doing?