In a right trianle with sides a, b and c we have
`a^2 + b^2 = c^2` the Pythagorean theorem
If we divide by `b^2` we get
`a^2/b^2 + 1 = c^2/b^2`
By definition `a/b = tan theta` and `b/c = cos theta` (which means `c/b = 1/(cos theta)`
`tan^2 theta + 1 = 1/(cos^2 theta)`
`tan^2 theta + 1 = sec^2 theta`
Explain why tan^2(theta)+1 = sec^2(theta)?
the expression can be written as:
sin^2(theta)/cos^2(theta) = 1/cos^2(theta)
Multiplying both sides by cos^2(theta), we get:
sin^2(theta)+cos^2(theta) = 1
which is an axiom.