Sin(30) = 1/2
Sin(45) = root(2)/2
Sin(60) = root(3)/2
Cos(30) = root(3)/2
Cos(45) = root(2)/2
Cos(60) = 1/2
Tan(30) = root(3)/3
Tan(45) = 1
Tan(60) = root(3)
Csc(30) = 2
Csc(45) = root(2)
Csc(60) = 2root(3)/3
Sec(30) = 2root(3)/3
Sec(45) = root(2)
Sec(60) = 2
Cot(30) = root(3)
Cot(45) = 1
Cot(60) = root(3)/3
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There are 6 basic trig functions.sin(x) = 1/csc(x)cos(x) = 1/sec(x)tan(x) = sin(x)/cos(x) or 1/cot(x)csc(x) = 1/sin(x)sec(x) = 1/cos(x)cot(x) = cos(x)/sin(x) or 1/tan(x)---- In your problem csc(x)*cot(x) we can simplify csc(x).csc(x) = 1/sin(x)Similarly, cot(x) = cos(x)/sin(x).csc(x)*cot(x) = (1/sin[x])*(cos[x]/sin[x])= cos(x)/sin2(x) = cos(x) * 1/sin2(x)Either of the above answers should work.In general, try converting your trig functions into sine and cosine to make things simpler.
sin(0) = 0, sin(90) = 1, sin(180) = 0, sin (270) = -1 cos(0) = 1, cos(90) = 0, cos(180) = -1, cos (270) = 0 tan(0) = 0, tan (180) = 0. cosec(90) = 1, cosec(270) = -1 sec(0) = 1, sec(180) = -1 cot(90)= 0, cot(270) = 0 The rest of them: tan(90), tan (270) cosec(0), cosec(180) sec(90), sec(270) cot(0), cot(180) are not defined since they entail division by zero.
sin(90°) = 1 cos(90°) = 0 tan(90°) = ∞ sec(90°) = ∞ csc(90°) = 1 cot(90°) = 0
They are co-functions meaning that 90 - sec x = csc x.
Provided that any denominator is non-zero, sin = sqrt(1 - cos^2)tan = sqrt(1 - cos^2)/cos sec = 1/cos cosec = 1/sqrt(1 - cos^2) cot = cos/sqrt(1 - cos^2)