Trigonometry Examples

$\arccos (v (1 - x^{2})) + \arcsin (\sqrt{1 - x^{2}})$

Step 1

Apply the distributive property.

$\arccos (v \cdot 1 + v (- x^{2})) + \arcsin (\sqrt{1 - x^{2}})$

Step 2

Multiply $v$ by $1$ .

$\arccos (v + v (- x^{2})) + \arcsin (\sqrt{1 - x^{2}})$

Step 3

Rewrite using the commutative property of multiplication.

$\arccos (v - v x^{2}) + \arcsin (\sqrt{1 - x^{2}})$

Step 4

Rewrite $1$ as $1^{2}$ .

$\arccos (v - v x^{2}) + \arcsin (\sqrt{1^{2} - x^{2}})$

Step 5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = x$ .

$\arccos (v - v x^{2}) + \arcsin (\sqrt{(1 + x) (1 - x)})$