Question

et «be any integer. Round to me to three dec mal places we appropriate. If there is no solucion, erter solve the equalion by factor ng. Enter your answers as a comma - separates list. NO SOLUTION. )

Answer 1

Problem

Solution

For this case we can do the following:

`(1)/(\cos\theta)\cdot(\sin\theta)/(\cos\theta)-\cos \theta\cdot(\cos\theta)/(\sin\theta)=\sin \theta`
`(\sin\theta)/(cos^2\theta)-(\cos^2\theta)/(\sin\theta)=\sin \theta`
`(\sin^2\theta-\cos^2\theta\cos^2\theta)/(\sin\theta\cos^2\theta)=\sin \theta`

then we can croos multiply:

`\sin ^2\theta-\cos ^2\theta\cos ^2\theta=\sin ^2\theta\cos ^2\theta`

then we can redistribute the terms and we got:

`\sin ^2\theta=\cos ^2\theta\cos ^2\theta+\sin ^2\theta\cos ^2\theta`

taking common factor cos^2 we got:

`\sin ^2\theta=\cos ^2\theta(\cos ^2\theta+\sin ^2\theta)`

Since:

`\sin ^2\theta+\cos ^2\theta=1`

We have:

`\sin ^2\theta=\cos ^2\theta`

And thae answer for this case is:

`\theta=(\pi)/(4)+\pi\text{ n}`