# Trigonometric Functions And Identities

Hi there,

I am struggling to solve for x in the following problem:-

Find all values of x in the interval 0<= x <= 360 for which: tan^2(x) = 5sec(x) - 2

I have used the identity tan^2(x) + 1 = sec^2(x) to get:

sec^2(x) - 1 = 5sec(x) - 2

and rearranged to get

sec^2(x) - 5sec(x) + 1 = 0

but I cant factor this or solve for x. Can anyone help please?

## Answers and Replies

Hurkyl
Staff Emeritus
Science Advisor
Gold Member
Can anyone help please?
Why did you spend all of that effort to turn it into a quadratic equation?

I assumed that I need to get all the trig functions of the same type before I can solve for x. Using the identity for sec^2(x) seemed the obvious choice...which lead me to a quadratic. I couldn't see how else to solve for x. I also tried converting everything in terms of cos (x) which was more messy. I may be mistaken, but from previous questions I have answered like this, tend to lead to a quadratic to factor for a solution/s for x.

Hurkyl
Staff Emeritus
Science Advisor
Gold Member
tend to lead to a quadratic to factor for a solution/s for x.
Is factoring the only method you know for solving quadratic equations, or do you know other methods?

Completing the square, or using the quadratic formula are another two methods.

Thanks, tried completing the square to solve the quadratic and this worked.