CHAPTER 20 KEY FORMULAS AND EQUATIONS

Basic trigonometric identities	$\sin θ = \frac{1}{\csc θ}$ (20.1)	$\tan θ = \frac{\sin θ}{\cos θ}$ (20.4)	$\sin^{2} θ + \cos^{2} θ = 1$ (20.6)
$\cos θ = \frac{1}{\sec θ}$ (20.2)	$\cot θ = \frac{\cos θ}{\sin θ}$ (20.5)	$1 + \tan^{2} θ = \sec^{2} θ$ (20.7)
$\tan θ = \frac{1}{\cot θ}$ (20.3)	$1 + \cot^{2} θ = \csc^{2} θ$ (20.8)
Sum and difference identities		$\sin (α + β) = \sin α \cos β + \cos α \sin β$ (20.9)
$\cos (α + β) = \cos α \cos β - \sin α \sin β$ (20.10)
$\sin (α - β) = \sin α \cos β - \cos α \sin β$ (20.11)
$\cos (α - β) = \cos α \cos β + \sin α \sin β$ (20.12)
$\tan (α \pm β) = \frac{\tan α \pm \tan β}{1 \mp \tan α \tan β}$ (20.13)
Double-angle formulas		$\sin 2 α = 2 \sin α \cos α$ (20.21)
$\cos 2 α = \cos^{2} α - \sin^{2} α$ (20.22)
$= 2 \cos^{2} α - 1$ (20.23)
$= 1 - 2 \sin^{2} α$ (20.24)
$\tan 2 α = \frac{2 \tan α}{1 - \tan^{2} α}$ (20.25)
Half-angle ...

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Basic Technical Mathematics, 11th Edition by Allyn J. Washington, Richard Evans