# Explain why tan^2(theta)+1 = sec^2(theta)?

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### 2 Answers

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)`

so

`tan^2 theta + 1 = 1/(cos^2 theta)`

which gives

`tan^2 theta + 1 = sec^2 theta`

### User Comments

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.