Question

Can anyone help me with 4 and 5? I don’t think I did them correctly

Answer 1

`\\ \tt\Rrightarrow tan^2x=3`

`\\ \tt\Rrightarrow tanx=√(3)`

`\\ \tt\Rrightarrow x=tan^(-1){√(3)}`

• x=π/3 or 2π/3

#5

`\\ \tt\Rrightarrow tanxsinx-tanx`

`\\ \tt\Rrightarrow tanx(sinx-1)`

`\\ \tt\Rrightarrow sinx/cosx(cos^2x)`

`\\ \tt\Rrightarrow sinxcosx`

Answer 2

4)
`x=(1)/(3) \pi \pm \pi n, \ x=(2)/(3) \pi \pm \pi n`

5)
`tan(x)[sin(x)-1]`

Explanation:

Question 4

`tan^2(x)=3`

square root both sides:

`\implies √( tan^2(x))=\pm √(3)`

`\implies tan(x)=\pm √(3)`

General solutions for
`tan(x)=√(3)`:

`\implies x=(1)/(3) \pi \pm \pi n`

General solutions for
`tan(x)=-√(3)`

`\implies x=(2)/(3) \pi \pm \pi n`

Combine all solutions:

`\implies x=(1)/(3) \pi \pm \pi n, \ x=(2)/(3) \pi \pm \pi n`

Question 5

`tan(x)sin(x)-tan(x)`

Factor out the common term
`tan(x)`:

`\implies tan(x)[sin(x)-1]`