(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: sin⁡(θ)−cos⁡(θ)+1sin⁡(θ)+cos⁡(θ)−1\frac{\sin\left( θ \right) - \cos\left( θ \right) + 1}{\sin\left( θ \right) + \cos\left( θ \right) - 1}

MathBot Answer:

Evaluated



sin⁡(θ)−cos⁡(θ)+1sin⁡(θ)+cos⁡(θ)−1=sin⁡(θ)−cos⁡(θ)+1sin⁡(θ)+cos⁡(θ)−1\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

sin⁡(θ)−cos⁡(θ)+1sin⁡(θ)+cos⁡(θ)−1=sin⁡(θ)sin⁡(θ)+cos⁡(θ)−1−cos⁡(θ)sin⁡(θ)+cos⁡(θ)−1+1sin⁡(θ)+cos⁡(θ)−1\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

sin⁡(θ)−cos⁡(θ)+1sin⁡(θ)+cos⁡(θ)−1=−−sin⁡(θ)+cos⁡(θ)−1sin⁡(θ)+cos⁡(θ)−1\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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