Trigonometric Identities and Equations

Question

Hello, I've been trying to solve this problem but cannot seem to understand it. The problem is as follows:

What are all the values of theta to the nearest degree in the interval 0 degrees is less than or equal to theta is less than or equal to 360 degrees?

2Tan^2(thetha)-Sec(thetha)-3=0

And

What are the values of theta, to the nearest degree, in the interval o degrees is less than or equal to thetha is less than 360 degrees

4Sin^2(thetha)=9Cos(thetha)+6

Thanks in advance!

Answer 1

I will not solve these for you, but I will tell you how to do them.

In the first one, 1+ tan²x = sec²x will resolve the sequation to a quadratic in sec x.

In the 2nd one sin²x + cos²x = 1 will resolve the equation to a quadratic equation in cos x.