Applying the trigonometric identity: $\displaystyle\frac{1}{\sec(\theta)}=\cos(\theta)$

When multiplying two powers that have the same base ($\cos\left(x\right)$), you can add the exponents

Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$

Divide fractions $\frac{\sin\left(x\right)}{\frac{1}{\sin\left(x\right)}}$ with Keep, Change, Flip: $a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}$

Applying the trigonometric identity: $\sin\left(\theta \right)^2-\cos\left(\theta \right)^2 = -\cos\left(2\theta \right)$