Question

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

Answer 1

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.

Answer 2

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

You'll see this better if I use latex.

$\frac{cos(x)}{1} * \frac{sin(x)}{cos(x)} * \frac{1}{sin(x)}$

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