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

asked by guest
on Nov 24, 2024 at 8:42 pm



You asked:

Evaluate the expression: \(\frac{\sin\left( θ \right) - \cos\left( θ \right) + 1}{\sin\left( θ \right) + \cos\left( θ \right) - 1}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{\sin\left( θ \right) - \cos\left( θ \right) + 1}{\sin\left( θ \right) + \cos\left( θ \right) - 1} = \frac{\sin{\left(θ \right)} - \cos{\left(θ \right)} + 1}{\sin{\left(θ \right)} + \cos{\left(θ \right)} - 1} \)

Expanded

\[\frac{\sin\left( θ \right) - \cos\left( θ \right) + 1}{\sin\left( θ \right) + \cos\left( θ \right) - 1} = \frac{\sin{\left(θ \right)}}{\sin{\left(θ \right)} + \cos{\left(θ \right)} - 1} - \frac{\cos{\left(θ \right)}}{\sin{\left(θ \right)} + \cos{\left(θ \right)} - 1} + \frac{1}{\sin{\left(θ \right)} + \cos{\left(θ \right)} - 1}\]

Factored

\[\frac{\sin\left( θ \right) - \cos\left( θ \right) + 1}{\sin\left( θ \right) + \cos\left( θ \right) - 1} = - \frac{- \sin{\left(θ \right)} + \cos{\left(θ \right)} - 1}{\sin{\left(θ \right)} + \cos{\left(θ \right)} - 1}\]

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