Simplify the trigonometric expression (1-2cos(y)^2)/(1-2cos(y)sin(y))

 Exercise

$\frac{1-2cos^2\left(y\right)}{1-2cos\left(y\right)sin\left(y\right)}$

 

Applying the trigonometric identity: $1-2\cos\left(\theta \right)^2 = -\cos\left(2\theta \right)$

$\frac{-\cos\left(2y\right)}{1-2\cos\left(y\right)\sin\left(y\right)}$

 

Using the sine double-angle identity: $\sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right)$

$\frac{-\cos\left(2y\right)}{1-2\cdot \left(\frac{1}{2}\right)\sin\left(2y\right)}$

 

Multiply the fraction and term in $-2\cdot \left(\frac{1}{2}\right)\sin\left(2y\right)$

$\frac{-\cos\left(2y\right)}{1+\frac{-2\cdot 1}{2}\sin\left(2y\right)}$

 

Multiply $-2$ times $1$

$\frac{-\cos\left(2y\right)}{1-\frac{2}{2}\sin\left(2y\right)}$

 

Divide $-2$ by $2$

$\frac{-\cos\left(2y\right)}{1-\sin\left(2y\right)}$

$\frac{-\cos\left(2y\right)}{1-\sin\left(2y\right)}$

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