Verify trig identity. show steps and give reason for each step. (cosx)(tanx)(cscx)=1

Tan(x) = sin(x) / cos(x)
Csc(x) = 1/ sin(x)

You'll see this better if I use latex.



Now just cancel numerators with denominations. They all disappear. The cancelations leave 1 on both the numerator and denominator.

Cosine = adjacent / hypotenuse
tangent = opposite / adjacent
cosecant = hypotenuse / opposite
So if we multiply these 3 we get a numerator of
adjacent * opposite * hypotenuseand a denominator ofhypotenuse * adjacent * opposite

We have a numerator and a denominator that equal each other giving us a value of 1.

In the first triangle 80+20+p=180 (since sum of all angles of a triangle is 180)so p= 80also in second triangle 55+45+q=180 (since sum of all angles of a triangle is 180)so q=80so we can conclude that p=80 degrees q=80 degrees so p=q=80 degreeshence option b is correct