Question

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

Answer 1

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

$\\ \tt\Rrightarrow tanx=\sqrt{3}$

$\\ \tt\Rrightarrow x=tan^{-1}{\sqrt{3}}$

• 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

Answer:

4)   $x=\dfrac{1}{3} \pi \pm \pi n, \ x=\dfrac{2}{3} \pi \pm \pi n$

5)  $tan(x)[sin(x)-1]$

Step-by-step explanation:

Question 4

$tan^2(x)=3$

square root both sides:

$\implies \sqrt{ tan^2(x)}=\pm \sqrt{3}$

$\implies tan(x)=\pm \sqrt{3}$

General solutions for $tan(x)=\sqrt{3}$:

$\implies x=\dfrac{1}{3} \pi \pm \pi n$

General solutions for $tan(x)=-\sqrt{3}$

$\implies x=\dfrac{2}{3} \pi \pm \pi n$

Combine all solutions:

$\implies x=\dfrac{1}{3} \pi \pm \pi n, \ x=\dfrac{2}{3} \pi \pm \pi n$

Question 5

$tan(x)sin(x)-tan(x)$

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

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