In addition to sine, cosine, and tangent, we have the trigonometric functions secant (sec), cosecant (csc), and cotangent (cot). We define these as follows:

Question

sec x= 1/cos x,

csc x=1/sin x,

cot x= cos x/sin x,

for those values of  where the right side is defined.

Explain why we must have  for any  such that  is not an integer multiple of .

Answer 1

sin² θ + cos² θ = 1 Pythagorean Identity

(sin² θ / sin² θ) + (cos² θ / sin² θ) = 1 / sin² θ

1 + cot² θ = csc²