in trigg how do i simplify?

Question

simplify problems like

sinθ * cscθ
or
cscθ/sinθ-cotθ/tanθ

anything would help

Answer 1

You need to know the definitions of the reciprocal functions:
secant: sec = 1/cos
cosecant: csc = 1/sin
cotangent: cot = 1/tan

You may also need the most basic trig identity: sin^2 + cos^2 = 1

If you know those, the problems are easy. The first one becomes just sinT * 1/sinT. The "sinT" cancels, so you're left with just 1.

The second is (1/sinT)/sinT - (1/tan)/tan
This is 1/(sinT)^2 - 1/(tanT)^2 or 1/(sinT)^2) - (cosT)^2/(sinT)^2
So you have [1 - (cosT)^2] / (sinT)^2.
Since sin^2 + cos^2 = 1, it's also true that sin^2 = 1 - cos^2.
So the top of the fraction is just (sinT)^2.
That means you have (sinT)^2/(sinT)^2, which is also equal to 1.