Question

Find all values of θ within the interval 0<θ 11 years ago

Answer 1

Welcome to OpenStudy @Questionmachine! :)

Answer 2

The equation can be expanded to:\[
\frac{\sin^2\theta}{\cos^2\theta} +\frac{\cos^2\theta}{\sin^2\theta} = 2
\]

Answer 3

Multiply both sides by \(\sin^2\theta\cos^2\theta\) and get \[
\sin^4\theta+\cos^4\theta=2\sin^2\theta\cos^2\theta
\]Interestingly enough... this is similar to \[
(a-b)^2 = a^2-2ab+b^2
\]

Answer 4

So it simplifies to: \[
\sin^2\theta - \cos^2\theta = 0 \implies \sin^2\theta = \cos^2\theta
\]

Answer 5

Or you can use double angle formula \[
\sin^2\theta - \cos^2\theta =0 \implies (1- \cos^2\theta) - \cos^2\theta =0 \implies 2\cos^2\theta = 1
\]

Answer 6

Thanks, Wio. But what is the final answer supposed to be ? What are the values that satisfy it ?

Answer 7

Well, you get \[
|\cos\theta| = \frac{1}{\sqrt2}
\]So you have to find values where \(0\lt \theta \lt \pi\)

Answer 8

So, the answer is 45 ? Sorry. I am a tad too slow at catching stuff.