How do you simplify csc theta cot theta?

Answer 1

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.