Формули за сбор и разлика на ъгъл

$cos (α \pm β) = cos α cos β \mp sin α sin β$

$sin (α \pm β) = sin α cos β \pm cos α sin β$

$tan (α \pm β) = \frac{tan α \pm tan β}{1 \mp tan α tan β}$

$cot (α \pm β) = \frac{cot α cot β \mp 1}{cot β \pm cot α}$

Формули за удвоения ъгъл

$sin (2 θ) = 2 sin θ cos θ$

$cos (2 θ) = cos^{2} θ - sin^{2} θ = 1 - 2 sin^{2} θ = 2 cos^{2} θ - 1$

$tan (2 θ) = \frac{2 tan θ}{1 - tan ^{2} θ}$

$cot (2 θ) = \frac{cot ^{2} θ - 1}{2 cot θ}$

$sin \frac{θ}{2} = \pm \frac{1 - cos θ}{2}$

$cos \frac{θ}{2} = \pm \frac{1 + cos θ}{2}$

$tan \frac{θ}{2} = \pm \frac{1 - cos θ}{1 + cos θ}$

$cot \frac{θ}{2} = \pm \frac{1 + cos θ}{1 - cos θ}$

$cos^{2} θ = \frac{1 + cos ( 2 θ )}{2}$

$sin^{2} θ = \frac{1 - cos ( 2 θ )}{2}$

$sin θ = \frac{2 tan \frac{θ}{2}}{1 + tan ^{2} \frac{θ}{2}}$

$cos θ = \frac{1 - tan ^{2} \frac{θ}{2}}{1 + tan ^{2} \frac{θ}{2}}$

$tan θ = \frac{2 tan \frac{θ}{2}}{1 - tan ^{2} \frac{θ}{2}}$

$cot θ = \frac{1 - tan ^{2} \frac{θ}{2}}{2 tan \frac{θ}{2}}$

$sin α cos β = \frac{sin ( α - β ) + sin ( α + β )}{2}$

$cos α cos β = \frac{cos ( α - β ) + cos ( α + β )}{2}$

$sin α sin β = \frac{cos ( α - β ) - cos ( α + β )}{2}$

$sin α \pm sin β = 2 sin \frac{α \pm β}{2} cos \frac{α \mp β}{2}$

$cos α + cos β = 2 cos \frac{α + β}{2} cos \frac{α - β}{2}$

$cos α - cos β = - 2 sin \frac{α + β}{2} sin \frac{α - β}{2}$