The Identities of Trigonometry

Another important part of trigonometry is the trigonometric identity. Trigonometric identities are used to prove equations are the same and are used to solve the equations. There is nothing tricky about trigonometry identity. Once you memorize the formulas below, you will do well on it.

Basics:

     sin^2x + cos^2x = 1
     tanx = sinx / cosx
     cotx = cosx /sinx
     secx = 1 / cosx
     cscx = 1 / sinx
     cotx = 1 / tanx
     1 + cot^2x = csc^2x
     tan^2x + 1 = sec^2x

Advanced:

     cos(a + b) = cos a cos b – sin a sin b
     cos(a - b) = cos a cos b + sin a sin b
     sin(a + b) = sin a cos b + cos a sin b
     sin(a - b) = sin a cos b - cos a sin b
     tan (a + b) = tan a + tan b / 1 – tan a tan b
     tan (a - b) = tan a + tan b / 1 + tan a tan b
     cos 2x = cos^2x – sin^2x
     cos 2x = 1 – 2 sin^2x
     cos 2x = 2 cos^2x – 1
     sin 2x = 2 sinx cosx
     tan 2x = 2tanx / 1 – tan^2x
     cos x/2 = +-Ö (1 + cosy / 2)
     sin x/2 = +- Ö (1 – cosy /2)
     tan x/2 = sin y / 1 + cos y
     tan x/2 = 1 – cosy / sin y
     sin 3x = 3 sin x – 4 sin^3 x
     cos 3x = 4 cos^3 x – 3 cos x

     sin a + sin b = 2 sin ( a + b / 2) cos ( a - b / 2)
     sin a - sin b = 2 cos ( a + b / 2) sin ( a - b / 2)
     cos a + cos b = 2 cos ( a + b / 2) cos ( a - b / 2)
     cos a – cos b = -2 sin ( a + b / 2) sin ( a - b / 2)

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