Properties

The Pythagorean identities are:

• cos[latex]^{2}[/latex](θ) + sin[latex]^{2}[/latex](θ) = 1
• 1 + tan[latex]^{2}[/latex](θ) = sec[latex]^{2}[/latex](θ)
• 1 + cot[latex]^{2}[/latex](θ) = cosec[latex]^{2}[/latex](θ)

The formulas for the sum and difference of two angles are:

• cos(θ + φ) = cos(θ) cos(φ) – sin(θ) sin(φ)
• cos(θ – φ) = cos(θ) cos(φ) + sin(θ) sin(φ)
• sin(θ + φ) = sin(θ) cos(φ) + sin(φ) cos(θ)
• sin(θ – φ) = sin(θ) cos(φ) – sin(φ) cos(θ)
• tan(θ + φ) = [latex]\dfrac{\textrm{tan}(\textit{θ}) + \textrm{tan}(\textit{φ})}{1 -\textrm{tan}(\textit{θ})\textrm{tan}(\textit{φ})}[/latex]
• tan(θ – φ) =[latex]\dfrac{\textrm{tan}(\textit{θ}) − \textrm{tan}(\textit{φ})}{1 +\textrm{tan}(\textit{θ})\textrm{tan}(\textit{φ})}[/latex]