Trigonometric Identities - Clavius

Trigonometric Identities

1. Basic Identities

$\sin^{2} α + \cos^{2} α = 1$

$\tan α = \frac{\sin α}{\cos α}$

2. Conjugate Form

Form	Conjugate	Result
$a + b$	$a - b$	$a^{2} - b^{2}$

3. Expansion and Factorization

$(a + b)^{2} = a^{2} + 2 a b + b^{2}$	$(a - b)^{2} = a^{2} - 2 a b + b^{2}$
$(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}$	$(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}$
$a^{2} - b^{2} = (a + b) (a - b)$	$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
	$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$

Exercise

--- Open this page ---