$\mathrm{sen}^{2} (a) + \cos^{2} (a) = 1$


$tg (a) = \frac{sen (a)}{\cos (a)}$


$cotg (a) = \frac{\cos (a) }{sen (a)}$


$sec (a) = \frac{1}{\cos (a)}$


$cossec (a) = \frac{1}{sen (a)}$

$tg^{2} (a) + 1 = sec^{2} (a)$


$cotg^{2} (a) +1 = cossec^{2} (a)$

$sen(a+b) = sen(a) \ . \cos (b) + sen(b) \ . \cos(a)$


$\cos (a+b) = \cos (a) \ . \cos (b) - sen(a) \ . sen(b)$


$tg(a+b) = \frac{tg(a) + tg(b)}{1-tg(a) \ . tg(b)}$

$sen(a-b) = sen(a) \ . \cos (b) - sen(b) \ . \cos (a)$


$\cos (a-b) = \cos (a) \ . \cos (b) + sen(a) \ . sen(b)$


$tg(a-b) = \frac{tg(a) - tg(b)}{1+tg(a) \ . tg(b)}$

$sen (a) + sen (b) = 2 sen \left( \frac{a+b}{2} \right) \ . \cos \left( \frac{a-b}{2} \right)$


$ \cos (a)+ \cos (b) = 2 \cos \left(\frac{a+b}{2} \right) \ . \cos \left(\frac{a-b}{2}\right)$


$tg (a) + tg (b) = \left( \frac{sen (a+b)}{\cos (a) \ . \cos (b)} \right)$

$ sen (a) - sen (b) = 2 sen \left( \frac{a-b}{2} \right) \ . \cos \left( \frac{a+b}{2} \right) $


$ \cos (a) - \cos (b) = -2 sen \left( \frac{a+b}{2} \right) \ . sen \left( \frac{a-b}{2} \right)$


$tg (a) -tg (b) = \left( \frac{sen (a-b)}{\cos (a) \ . \cos (b)} \right) $

$sen \left( \frac{a}{2} \right) = \pm \sqrt[]{\frac{1- \cos (a)}{2}}$


$\cos \left( \frac{a}{2} \right) = \pm \sqrt[]{\frac{1+\cos (a)}{2}}$


$tg \left( \frac{a}{2} \right) = \pm \sqrt[]{\frac{1- \cos (a)}{1+ \cos (a)}}$

$sen(2a) = 2sen(a) \ . \cos (a)$


$\cos (2a) = \cos^{2} (a) - sen^{2}(a)$


$tg(2a) = \frac{2tg(a)}{1-tg^{\style{font-family:Arial; font-size:31px;}{2}}(a)}$

$sen(3a) = 3sen(a)-4sen^{3}(a)$


$\cos (3a) = 4 \cos^{3} (3a) - 3 \cos (a)$


$tg (3a) = \frac{3tg (a)-tg^{3}(a)}{1-3tg^{\style{font-family:Arial; font-size:30px;}2}(a)}$

$sen(4a) =4sen(a) \ . \cos (a) -8sen^{3} (a) \ . \cos (a) $


$\cos (4a) = 8 \cos^{4} (a) - 8 \cos^{2} (a) +1$


$tg (4a) = \frac{4tg (a)- 4tg^{3}(a)}{1-6tg^{\style{font-family:Arial; font-size:30px;}2}(a)+tg^{\style{font-family:Arial; font-size:30px;}4} (a)}$

$sen(5a) = 5sen(a) - 20sen^{3} (a) +16sen^{5} (a)$


$\cos (5a) = 16 \cos^{5} (a) - 20 \cos^{3} (a) +5 \cos (a)$


$tg (5a) = \frac{tg^{5}(a) - 10tg^{3}(a) +5tg (a)}{1-10tg^{\style{font-family:Arial; font-size:30px;}2}(a)+5tg^{\style{font-family:Arial; font-size:30px;}4} (a)}$

$sen (-a) = -sen(a)$


$\cos (-a) = \cos (a)$


$tg(-a) = -tg(a)$


$cossec(-a) = -cossec(a)$


$sec(-a) = sec (a)$


$cotg (-a) = -cotg (a)$

$sen (90° \hspace{-0.3em} -a) = \cos (a)$


$\cos (90° \hspace{-0.3em} -a) = sen (a)$


$tg (90° \hspace{-0.3em} -a) = cotg (a)$


$cotg (90° \hspace{-0.3em} -a) = tg (a)$


$sec (90° \hspace{-0.3em} -a) = cossec (a)$


$cossec (90° \hspace{-0.3em} -a) = sec (a)$

$sen (360° \hspace{-0.3em} +a) = sen (a)$


$\cos (360° \hspace{-0.3em} +a) = \cos (a)$


$tg (180° \hspace{-0.3em} +a) = tg(a)$


$cotg (180° \hspace{-0.3em} +a) = cotg(a)$


$sec (360° \hspace{-0.3em} +a) = sec(a)$


$cossec (360° \hspace{-0.3em} +a) = cossec(a)$

$sen (a) \ . sen (b) = \frac { \cos (a-b) - \cos(a+b)}{2}$


$\cos (a) \ . \cos (b) = \frac {\cos (a-b) + \cos (a+b)}{2}$


$sen (a) \ . \cos (b) = \frac {sen (a-b)+sen (a+b)}{2}$


$tg (a) \ . tg(b) = \frac {tg (a) + tg(b)}{cotg(a) + cotg(b)}$


$cotg(a) \ . cotg(b) = \frac {cotg(a) + cotg(b)}{tg (a) + tg (b)}$


$tg(a) \ . cotg(b) = \frac {tg (a) + cotg (b)}{cotg (a) + tg (b)}$

$sen^{2} (a) = \frac{1-cos (2a)}{2}$


$sen^{3} (a) = \frac{3sen (a) -sen(3a)}{4}$


$sen^{4} (a) = \frac{\cos (4a) -4 \cos (2a) + 3}{8}$


$sen^{5} (a) = \frac{10sen (a) -5 sen (3a) + sen(5a)}{16}$


$sen^{6} (a) = \frac{10 - 15 \cos (2a) +6 \cos (4a) -cos (6a)}{32}$


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


$\cos^{3} (a) = \frac{3 \cos (a) +cos(3a)}{4}$


$\cos^{4} (a) = \frac{\cos (4a) +4 \cos (2a) + 3}{8}$


$\cos^{5} (a) = \frac{10 \cos (a) +5 sen (3a) + \cos (5a)}{16}$


$\cos^{6} (a) = \frac{10 + 15 \cos (2a) +6 \cos (4a) + cos (6a)}{32}$