Trigonometry Examples

$\frac{\sin^{3} (θ) + \cos^{3} (θ)}{\sin (θ) + \cos (θ)}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = \sin (θ)$ and $b = \cos (θ)$ .

$\frac{(\sin (θ) + \cos (θ)) (\sin^{2} (θ) - \sin (θ) \cos (θ) + \cos^{2} (θ))}{\sin (θ) + \cos (θ)}$

Step 1.2

Simplify.

Tap for more steps...

Step 1.2.1

Rearrange terms.

$\frac{(\sin (θ) + \cos (θ)) (- \sin (θ) \cos (θ) + \sin^{2} (θ) + \cos^{2} (θ))}{\sin (θ) + \cos (θ)}$

Step 1.2.2

Apply pythagorean identity.

$\frac{(\sin (θ) + \cos (θ)) (- \sin (θ) \cos (θ) + 1)}{\sin (θ) + \cos (θ)}$

Step 2

Cancel the common factor of $\sin (θ) + \cos (θ)$ .

Tap for more steps...

Step 2.1

Cancel the common factor.

$\frac{(\sin (θ) + \cos (θ)) (- \sin (θ) \cos (θ) + 1)}{\sin (θ) + \cos (θ)}$

Step 2.2

Divide $- \sin (θ) \cos (θ) + 1$ by $1$ .

$- \sin (θ) \cos (θ) + 1$