Trigonometry Examples

$(1 - \sin (θ)) (1 + \sin (θ))$

Step 1

Expand $(1 - \sin (θ)) (1 + \sin (θ))$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$1 (1 + \sin (θ)) - \sin (θ) (1 + \sin (θ))$

Step 1.2

Apply the distributive property.

$1 \cdot 1 + 1 \sin (θ) - \sin (θ) (1 + \sin (θ))$

Step 1.3

Apply the distributive property.

$1 \cdot 1 + 1 \sin (θ) - \sin (θ) \cdot 1 - \sin (θ) \sin (θ)$

Step 2

Simplify and combine like terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Multiply $1$ by $1$ .

$1 + 1 \sin (θ) - \sin (θ) \cdot 1 - \sin (θ) \sin (θ)$

Step 2.1.2

Multiply $\sin (θ)$ by $1$ .

$1 + \sin (θ) - \sin (θ) \cdot 1 - \sin (θ) \sin (θ)$

Step 2.1.3

Multiply $- 1$ by $1$ .

$1 + \sin (θ) - \sin (θ) - \sin (θ) \sin (θ)$

Step 2.1.4

Multiply $- \sin (θ) \sin (θ)$ .

Tap for more steps...

Step 2.1.4.1

Raise $\sin (θ)$ to the power of $1$ .

$1 + \sin (θ) - \sin (θ) - (\sin^{1} (θ) \sin (θ))$

Step 2.1.4.2

Raise $\sin (θ)$ to the power of $1$ .

$1 + \sin (θ) - \sin (θ) - (\sin^{1} (θ) \sin^{1} (θ))$

Step 2.1.4.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$1 + \sin (θ) - \sin (θ) - {\sin (θ)}^{1 + 1}$

Step 2.1.4.4

Add $1$ and $1$ .

$1 + \sin (θ) - \sin (θ) - \sin^{2} (θ)$

Step 2.2

Subtract $\sin (θ)$ from $\sin (θ)$ .

$1 + 0 - \sin^{2} (θ)$

Step 2.3

Add $1$ and $0$ .

$1 - \sin^{2} (θ)$

Step 3

Apply pythagorean identity.

$\cos^{2} (θ)$