$\frac{x-1}{x+3}.\frac{x^2+4x+3}{x^2-1}$

$\csc^2\left(x\right)\left(1-cos^2x\right)=1$

$\frac{-\sin^2\left(x\right)+\csc^2\left(x\right)-\cos^2\left(x\right)}{\cot\left(x\right)}$

$20a^2-45$

$\int\left(8x^{2}-3x+2\right)\left(2x-3\right)dx$

$x\frac{dy}{dx}=\left(x\sin\left(x\right)-y\right)$

$\frac{\sin\left(x\right)-\cos\left(x\right)}{\sin\left(x\right)+\cos\left(x\right)}=\frac{1-\cot\left(x\right)}{1+\cot\left(x\right)}$