Trigonometry Examples

$\sqrt{\cos (a) \sin^{2} (a)} - \sqrt{\cos^{7} (a)}$

Step 1

Reorder $\cos (a)$ and $\sin^{2} (a)$ .

$\sqrt{\sin^{2} (a) \cos (a)} - \sqrt{\cos^{7} (a)}$

Step 2

Pull terms out from under the radical.

$\sin (a) \sqrt{\cos (a)} - \sqrt{\cos^{7} (a)}$

Step 3

Rewrite $\cos^{7} (a)$ as ${(\cos^{3} (a))}^{2} \cos (a)$ .

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Step 3.1

Factor out $\cos^{6} (a)$ .

$\sin (a) \sqrt{\cos (a)} - \sqrt{\cos^{6} (a) \cos (a)}$

Step 3.2

Rewrite $\cos^{6} (a)$ as ${(\cos^{3} (a))}^{2}$ .

$\sin (a) \sqrt{\cos (a)} - \sqrt{{(\cos^{3} (a))}^{2} \cos (a)}$

Step 4

Pull terms out from under the radical.

$\sin (a) \sqrt{\cos (a)} - \cos^{3} (a) \sqrt{\cos (a)}$