Solve f(x)=sin^2x-sin^2x(x-pi/6)^v

$$f ( x ) = \sin ^ { 2 } x - \sin ^ { 2 } x ( x - \frac { \pi } { 6 } ) ^ { v }$$

Factor

$$\left(-\sin(x\times \left(\frac{6x-\pi }{6}\right)^{v})+\sin(x)\right)\left(\sin(x\times \left(\frac{6x-\pi }{6}\right)^{v})+\sin(x)\right)$$

Solution Steps

The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(\sin(x)-\sin(x\times \left(\frac{6x-\pi }{6}\right)^{v})\right)\left(\sin(x)+\sin(x\times \left(\frac{6x-\pi }{6}\right)^{v})\right)$$

Evaluate

$$-\left(\sin(x\times \left(\frac{6x-\pi }{6}\right)^{v})\right)^{2}+\left(\sin(x)\right)^{2}$$