【一般の三角関数の公式】

sin(-x) = -sin(x), sin(π/2-x) =  cos(x), sin(π-x) =  sin(x),
cos(-x) =  cos(x), cos(π/2-x) =  sin(x), cos(π-x) = -cos(x),
                   sin(π/2+x) =  cos(x), sin(π+x) = -sin(x),
                   cos(π/2+x) = -sin(x), cos(π+x) = -cos(x),

sin(x)^2 + cos(x)^2 = 1

加算公式
sin(x+y) = sin(x)cos(y)+cos(x)sin(y),
cos(x+y) = cos(x)cos(y)-sin(x)sin(y),

積和公式
2sin(x)cos(y) =  sin(x+y) + sin(x-y),
2cos(x)sin(y) =  sin(x+y) - sin(x-y),
2cos(x)cos(y) =  cos(x+y) + cos(x-y),
2sin(x)sin(y) = -cos(x+y) + cos(x-y),

和積公式
sin(x)+sin(y) =  2sin( (x+y)/2 ) ・ cos( (x-y)/2 ),
sin(x)-sin(y) =  2cos( (x+y)/2 ) ・ sin( (x-y)/2 ),
cos(x)+cos(y) =  2cos( (x+y)/2 ) ・ cos( (x-y)/2 ),
cos(x)-cos(y) = -2sin( (x+y)/2 ) ・ sin( (x-y)/2 ),

倍角公式
sin(2x) = 2sin(x)cos(x), 
cos(2x) = cos(x)^2 - sin(x)^2 = 2cos(x)^2 - 1 = 1 - 2sin(x)^2

半角公式
sin(x/2)^2 = ( 1-cos(x) )/2,
cos(x/2)^2 = ( 1+cos(x) )/2

【球面三角法】
球面の三角形ＡＢＣの内角をa,b,c, 対辺をα,β,γとするとき、次のような関係が
成立する。

sin(a):sin(b):sin(c) = sin(α):sin(β):sin(γ)      　  正弦公式
cos(a)  =  cos(b)cos(c)   + sin(b)sin(c)cos(α),etc.  　余弦公式
cos(α) = -cos(β)cos(γ) + sin(β)sin(γ)cos(a),etc.   　 〃
sin(a)cos(β) = cos(b)sin(c) - sin(b)cos(c)cos(α),etc. 正弦余弦公式