Solve (1-cost)*sint*sint*(2cost-1)+(1-cost)cost(sin^2t-cos^2t+cost)

$$( 1 - \cos t ) \cdot \sin t \cdot \sin t \cdot ( 2 \cos t - 1 ) + ( 1 - \cos t ) \cos t ( \sin ^ { 2 } t - \cos ^ { 2 } t + \cos t )$$

Factor

$$\left(-\cos(t)+1\right)\left(\sin(t\sin(t\left(2\cos(t)-1\right)))+\cos(t\left(\cos(t)-\cos(2t)\right))\right)$$

Solution Steps

Factor out 1-\cos(t).

$$\left(1-\cos(t)\right)\left(\sin(t\sin(t\left(2\cos(t)-1\right)))+\cos(t\left(\cos(t)-\cos(2t)\right))\right)$$

Evaluate

$$\left(-\cos(t)+1\right)\left(\sin(t\sin(t\left(2\cos(t)-1\right)))+\cos(t\left(\cos(t)-\cos(2t)\right))\right)$$