# pls tell all formulas related to trignometry.................  i want to know all formulas....................

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to know the basic formula of trigonometry:

`sin^ 2 alpha + cos^2 alpha = 1`

Dividing this formula by sin^2 alpha both sides yields:

`1 + cos^2 alpha/sin^2 alpha= 1/sin^2 alpha`

Replacing `cos^2 alpha/sin^2 alpha`  by `cot^2`  `alpha`  yields:

`1 + cot^2 alpha = 1/sin^2 alpha`

You should get the following formula, using like algorithm:

`tan^2 alpha + 1 = 1/cos^2 alpha`

The following trigonometric formulas are of the most use:

`sin alpha + sin beta = 2 sin (alpha + beta)/2 * cos (alpha- beta)/2`

`` `sin alpha- sin beta = 2cos (alpha + beta)/2 *sin (alpha- beta)/2`

`cosalpha +cos beta = 2cos (alpha + beta)/2 * cos (alpha- beta)/2`

`cosalpha-cos beta = -2sin (alpha + beta)/2 * cos (alpha- beta)/2`

You need to know the following formulas:

`sin 2 alpha = 2 sin alpha*cos alpha`

`cos2 alpha = cos^2 alpha - sin^2 alpha`

The formulas of double the argument alpha may be get if `2 alpha = alpha + alpha`  such that:

`sin 2alpha = sin(alpha + alpha) = sin alpha*cos alpha + sin alpha*cos alpha = 2 sin alpha*cos alpha`

`sin 3 alpha = 3 sin alpha - 4 sin^3 alpha`

`cos 3 alpha = 4 cos^3 alpha - 3 cos alpha`

`` `sin^2 alpha/2 = (1 - cos alpha)/2`

`` `cos^2 alpha/2 = (1+ cos alpha)/2`