Question

Solve the equation. tan^2θ=1

Answer 1

Given:

`\tan ^2\theta=1`

Aim:

`We\text{ n}eed\text{ to find the value of }\theta.`

Step-by-step explanation:

Take square root on both sides of the given equation.

`\sqrt[]{\tan^2\theta}=\sqrt[]{1}`
`\tan \theta=\pm1`

`\tan \theta=1,\text{ and }\tan \theta=-1`
`\text{Use }\tan ((\pi)/(4))=1,\tan (\pi+(\pi)/(4))=1,\text{ }\tan (\pi-(\pi)/(4))=-1,\text{ and }\tan ((3\pi)/(2)-(\pi)/(4))=-1.`

`\text{Use }\tan ((\pi)/(4))=1,\tan ((5\pi)/(4))=1,\text{ }\tan ((3\pi)/(4))=-1,\text{ and }\tan ((7\pi)/(4))=-1.`

`\tan \theta=\tan ((\pi)/(4)),\text{ }\tan \theta=\tan ((5\pi)/(4)),\tan \theta=\tan ((3\pi)/(4)),\text{ and }\tan \theta=\tan ((7\pi)/(4)).`
`\theta=(\pi)/(4),(5\pi)/(4),(3\pi)/(4),(7\pi)/(4)\text{.}`

Final answer:

The solution set is

`(\pi)/(4),(3\pi)/(4),(5\pi)/(4),(7\pi)/(4).`