User:Joerite/Trig


 * 1) $$tan \theta=\frac{sin \theta}{cos \theta}=\frac{1}{cot \theta}$$
 * 2) $$cot \theta=\frac{cos \theta}{sin \theta}=\frac{1}{tan \theta}$$
 * 3) $$sec \theta=\frac{1}{cos \theta} cos \theta=\frac{1}{sec \theta}$$
 * 4) $$csc \theta=\frac{1}{cos \theta} sin \theta=\frac{1}{csc \theta}$$
 * 5) $$\bigstar sin^2 \theta+cos^2 \theta=1$$
 * 6) *$$sin^2 \theta=1 - cos^2 \theta$$
 * 7) *$$cos^2 \theta=1 - sin^2 \theta$$
 * 8) $$sec^2 \theta-tan^2 \theta=1$$
 * 9) *$$sec^2 \theta=1 + tan^2 \theta$$
 * 10) *$$tan^2 \theta=sec^2 \theta -1 $$
 * 11) $$csc^2 \theta=cot^2 \theta =1$$
 * 12) *$$csc^2 \theta=1 + cot^2 \theta$$
 * 13) *$$cot^2 \theta=csc^2 \theta -1 $$
 * 14) $$cos( \alpha \pm \beta )=cos \alpha ~ cos \beta \mp sin \alpha ~ sin \beta$$
 * 15) $$sin( \alpha \pm \beta )=sin \alpha ~ cos \beta \mp cos \alpha ~ sin \beta$$
 * 16) $$tan( \alpha \pm \beta )=\frac{tan \theta \pm tan \beta}{1 \mp tan \alpha ~ tan \beta}$$
 * 17) cos(-x)=cos x
 * 18) sin(-x)= -sin x
 * 19) tan(-x)= -tan x
 * 20) $$cos 2 \theta=cos^2 \theta - sin^2 \theta $$
 * 21) *$$=2cos^2 \theta -1$$
 * 22) *$$=1- 2 sin^2 \theta$$
 * 23) $$sin ~ 2 \theta= 2sin \theta ~ cos \theta$$
 * 24) $$tan ~ 2 \theta= \frac{2tan \theta}{1-tan^2 \theta}$$
 * 25) $$cos \frac{\theta}{2}=\pm \sqrt{\frac{1}{2} \left ( 1 + cos \theta \right )}$$
 * 26) $$sin \frac{\theta}{2}=\pm \sqrt{\frac{1}{2} \left ( 1 - cos \theta \right )}$$
 * 27) $$tan \frac{\theta}{2}=\frac{1-cos \theta}{sin \theta}=\frac{sin \theta}{1+ cos \theta}$$
 * 28) $$2 cos \alpha ~ cos \beta =cos \left ( \alpha - \beta \right ) + cos \left ( \alpha + \beta \right )$$
 * 29) *$$cos ~ x + cos ~ y = 2 cos \left ( \frac{x+y}{2} \right ) cos \left ( \frac{x-y}{2} \right )$$
 * 30) $$2 sin \alpha ~ sin \beta =cos \left ( \alpha - \beta \right ) - cos \left ( \alpha + \beta \right )$$
 * 31) *$$cos ~ x - cos ~ y = 2 sin \left ( \frac{x+y}{2} \right ) sin \left ( \frac{x-y}{2} \right )$$
 * 32) $$2 sin \alpha ~ cos \beta =sin \left ( \alpha + \beta \right ) + cos \left ( \alpha - \beta \right )$$
 * 33) *$$sin ~ x + sin ~ y = 2 sin \left ( \frac{x+y}{2} \right ) cos \left ( \frac{x-y}{2} \right )$$
 * 34) $$2 cos \alpha ~ sin \beta =sin \left ( \alpha + \beta \right ) - cos \left ( \alpha - \beta \right )$$
 * 35) *$$sin ~ x - sin ~ y = 2 cos \left ( \frac{x+y}{2} \right ) sin \left ( \frac{x-y}{2} \right )$$