trig identities

• tan u/2

  (1-cos u)/sin u; = sin u/ (1+cos u)
• cos u/2

  +- sqrt (1+cos u)/2
• sin u/2

  +- sqrt (1-cos u)/2
• tan ^2 x

  (1-cos2x)/(1+cos2x)
• sin^2 x

  (1-cos 2x)/2
• tan 2x

  2tanx/(1-tan^2 x)
• cos2x

  cos^2 x- sin^2 x; = 1-2sin^2x; = 2 cos^2 x-1
• sin 2x

  2sin x cosx
• cos x- cos y

  -2sin (x+y)/2 sin (x-y)/2
• cosx+ cos y

  2 cos (x+y)/2 cos (x-y)/2
• sinx- siny

  2 cos (x+y)/2cos (x-y)/2
• sin x+ sin y

  2sin (x+y)/2 cos (x-y)/2
• sin u sin v

  1/2 [cos (u+v)- cos (u+v)]
• cos u cos v

  1/2[cos (u+v)+ cos (u-v)]
• cos u sin v

  1/2 [sin (u+v)- sin (u-v)]
• sin u cos v

  1/2 [sin (u+v) + sin (u-v)]
• tan (s-t)

  (tan s - tan t)/(1+ tan s tan t)
• tan (s+t)

  (tan s + tan t )/ (1-tan s tan t)
• cos (s-t)

  cos s cos t+ sin s sin t
• cos (s+t)

  cos s cos t- sin s sin t
• sin (s-t)

  sin s cos t- cos s sin t
• sin (s+t)

  sin s cos t+ cos s sin t
• csc (pi/2 - u)

  sec u
• cot (pi/2-u)

  tan u
• tan (pi/2-u)

  cot u
• cos (pi/2-u)=

  sin u
• sin (pi/2 - u)=

  cos u
• tan (-x)

  -tanx
• cos (-x)

  cosx
• 1+cot^2 x=


  csc^2 x
• tan^2 x+1=


  sec^2 x
• sin(-x)

  -sinx
• sin^2x+cos^2x=

  1
• cotx=

  cosx/sinx
• tan x=

  sinx/cosx
• cot x=

  1/tanx
• sec x=

  1/cos
• csc x=

  1/sin
• tan u/2

  (1-cos u)/sin u; = sin u/ (1+cos u)
• cos u/2

  +- sqrt (1+cos u)/2