How does the Sine A divided by the Cos A equal the Tan of A?

Question

sine45 divided by cos45 equal the same as tan 45

Answer 1

In a triangle with horizontal leg = x, vertical leg = y and hypotenuse = R

sin{theta} = y/R
cos{theta} = x/R
tan{theta} = y/x

from this, if you divide sin/cos then the R's cancel and you are left with y/x which just so happens to equal tangent.

Answer 2

because function Tan(x) is defined Sin(x) / Cos(x)...
try to drow a circle and identify these things in the drawing, this will help you understand

Answer 3

Lets say we have a right triangle with sides A,B,C (where A=B and C is the biggest side and the angle A is between the sides B and C and ):
CosA=B/C (1)
SinA=A/C (2)
TanA=SinA/CosA=(using (2),(1))=(A/C)/(B/C)=(A*C)/(B*C)=A/B=A/A=1