Question

Select the correct answer.Which of the following is a solution to

Answer 1

`\tan ^2x-1=0`

Factorizing the left expression using difference of two squares,

`\tan ^2x-1^2=0`
`(\tan x+1)(\tan x-1)=0_{}`
`\tan x+1=0\text{ or tanx-1=0}`
`\begin{gathered} \tan x=-1\text{ or tanx=1} \\ x=\tan ^(-1)(-1)orx=\tan ^(-1)(1) \end{gathered}`
`x=-45^0orx=45^0`

Hence from the given options, the value of x is 45°.

Option A is the correct answer.