Question

half angle formula help

Answer 1

but i have trouble getting here, specifically where does the 1/2 come from with the double angle formula

Answer 2

it's just an identity.
cos^2(x) = (1/2) (1 + cos(2x))

Answer 3

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

Answer 4

The identity allows you to do that substitution

Answer 5

yeah thanks.

Answer 6

\[=\int\limits \left( \frac{ 1+\cos (4t) }{ 2 } \right)^2 dt\]

Answer 7

\[=\int\limits \frac{ 1+2\cos 4t+\cos ^{2}\left( 4t \right) }{ 4 }dt\]
\[=\frac{ 1 }{ 4 }\int\limits dt+\frac{ 2 }{ 4 }\int\limits \cos (4t)dt+\frac{ 1 }{ 8 }\int\limits 2\cos ^{2}\left( 4 t \right)dt=?\]