Question

Solve 1- sin 2 theta/ 1-cos theta= -cos theta

Answer 1

use parenthesis please

Answer 2

1-(sin 2 theta) / (1-cos theta) = -cos theta

Answer 3

1+cosx=sin2x/(1-cosx)
1-(cosx)^2=2sinxcosx
(sinx)^2=2sinxcosx
sinx=2cosx
tanx=2
x=arctan2
x=63.43 degree or 1.107 radians

Answer 4

\[1 - \frac{sin(2\theta)}{1-cos(\theta)} = -cos(\theta)\]
\[1 +cos(\theta) = \frac{sin(2\theta)}{1-cos(\theta)}\]
\[(1 +cos(\theta))(1-cos(\theta)) = \frac{sin(2\theta)}{1-cos(\theta)}*(1-cos(\theta))\]
\[1 -cos^2(\theta) = sin(2\theta)\]
note that \[1 = sin^2(\theta) + cos^2(\theta) \]
therefore \[1 -cos^2(\theta) = sin^2(\theta)\]
so plug that back into the orginal equation \[sin^2(\theta) = sin(2\theta)\]
also note that
\[2cos(\theta)sin(\theta) = sin(2\theta)\]
therefore
\[sin^2(\theta) = 2cos(\theta)sin(\theta)\]
divide by \[sin(\theta)\] and you get \[sin(\theta)=2cos(\theta)\]
divide by \[cos(\theta)\]and you get \[tan(\theta)=2\]
do a little \[tan^{-1}(\theta)=tan^{-1}(2)\] and you've solved for theta

Answer 5

Thank you(:

Answer 6

good job