Solve sinx/1^4-sin2x/2^4+sin3x/3^4

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

Factor

$$\frac{\sin(x)\left(\cos(x)\left(32\cos(x)-81\right)+640\right)}{648}$$

Solution Steps

Calculate 1 to the power of 4 and get 1.

$$factor(\frac{\sin(x)}{1}-\frac{\sin(2x)}{2^{4}}+\frac{\sin(3x)}{3^{4}})$$

Anything divided by one gives itself.

$$factor(\sin(x)-\frac{\sin(2x)}{2^{4}}+\frac{\sin(3x)}{3^{4}})$$

Calculate 2 to the power of 4 and get 16.

$$factor(\sin(x)-\frac{\sin(2x)}{16}+\frac{\sin(3x)}{3^{4}})$$

Calculate 3 to the power of 4 and get 81.

$$factor(\sin(x)-\frac{\sin(2x)}{16}+\frac{\sin(3x)}{81})$$

Factor out \frac{1}{1296}.

$$\frac{1296\sin(x)-81\sin(2x)+16\sin(3x)}{1296}$$

Evaluate

$$\frac{\sin(x)\left(\cos(x)\left(32\cos(x)-81\right)+640\right)}{648}$$