Question

How do you solve the following equation `sec(x/2)=cos(x/2)` in the interval [0, 2pi]?

Answer 1

`x = 0 and x = 2pi`.

Explanation:

A number (cosine ) and its reciprocal ( secant ) are equal.

So, the cosine is `+- 1`.

Here, `cos (x/2) = +-1`.

`x/2 = 0 and pi in [0, pi]`.

So, `x = 0 and 2pi in [0, 2pi]`.