Question #b4f35

1 Answer
Feb 12, 2018

x=0, 3/4pi, pi, 7/4pi

Explanation:

We want to find the solutions of the equation

sec^2(x)+tan(x)=1

Use the trigonmetric identity color(blue)(sec^2(x)=tan^2(x)+1)

tan^2(x)+1+tan(x)=1

<=>tan^2(x)+tan(x)=0

<=>tan(x)(tan(x)+1)=0

Therefore

tan(x)=0 or tan(x)=-1

By the inverse tangent with x in [0,2pi)

x=0, 3/4pi, pi, 7/4pi