Solve 10sin(2t+pi/6)+5cos(3t+pi/4)

$$10 \sin ( 2 t + \frac { \pi } { 6 } ) + 5 \cos ( 3 t + \frac { \pi } { 4 } )$$

Factor

$$\frac{5\left(-3\sqrt{2}\sin(t)\left(\cos(t)\right)^{2}-3\sqrt{2}\cos(t)\left(\sin(t)\right)^{2}+\sqrt{2}\left(\sin(t)\right)^{3}+\sqrt{2}\left(\cos(t)\right)^{3}+2\sqrt{3}\sin(2t)+2\cos(2t)\right)}{2}$$

Solution Steps

Factor out 5.

$$5\left(2\sin(\frac{12t+\pi }{6})+\cos(\frac{12t+\pi }{4})\right)$$

Evaluate

$$\frac{5\sqrt{2}\left(-3\sin(t)\left(\cos(t)\right)^{2}-3\cos(t)\left(\sin(t)\right)^{2}+\left(\sin(t)\right)^{3}+\left(\cos(t)\right)^{3}+\sqrt{2}\sqrt{3}\sin(2t)+\sqrt{2}\cos(2t)\right)}{2}$$