Question

Help?

Find all solutions in the interval [0, 2pi).

sec^2 x – 2 = tan^2 x

Answer 1

This is not a calculation problem. This is a paying attention problem.

Really Big Hint: \(\sec^{2}(x) - \tan^{2}(x) = 1\)

You just have to see those easy ones and reach out and grab them!

Answer 2

are you sure this is the question?

Answer 3

rearranging gives
\[\sec^{2} x - \tan^{2} x = 2\]
which is false .... thus No solution

Answer 4

if so, there is no solution
subtract \(\tan^2(x)\) from both sides, get
\[\sec^2(x)-\tan^2(x)-2=0\]\[1-2=0\]
\[-1=0\] no solution

Answer 5

But wouldnt sec^2 x - 2 tan^2 x = 2?

Answer 6

Oooh okay, nevermind. I understand. Thank you :o)

Answer 7

you only have \(\tan^2(x)\) on the right, yes?

Answer 8

Yeah, I got confused with the -2 on the left.