Question

Fint the value of theta in each of the following
Root3 tan 2theta - 3 = 0​

Answer 1

Answer:

√3 tan2theta=3

tan2 theta=3/√3

tan2 theta=1/√3

tan2 theta=tan 30°

2theta=30°

theta=15°

Step-by-step explanation:

hope it helps you!!

Answer 2

$\mathrm{\bold{I \:hope\: it \:helps\: you}}$

$\mathrm{\bold{please\: mark\:it\:as\: brainliest}}$

∴$\sqrt{3}$ tan2θ - 3 = 0

∴$\sqrt{3}$ tan2θ = 0 + 3

∴$\sqrt{3}$ tan2θ = 3

∴tan2θ = $\frac{3}{\sqrt{3}}$

Now,

Multiply $\frac{3}{\sqrt{3}}$ by its conjugate term,

$\bold{=}$ $\frac{3}{\sqrt{3}}$ $\mathrm{\bold{\mathrm{×}}}$ $\frac{\sqrt{3}}{\sqrt{3}}$

$\bold{=}$ $\frac{{3}\sqrt{3}}{{\sqrt{3}}× {\sqrt{3}}}$

$\bold{=}$ $\frac{{3}\sqrt{3}}{3}$

$\bold{=}$ $\frac{\sqrt{3}}{1}$

$\bold{=}$ $\sqrt{3}$

∴$\bold{Now,}$

∴tan2θ = $\sqrt{3}$

∴tan2θ = tan60....(∵ tan60°= $\sqrt{3}$ )

∴tanθ = $\frac{tan60}{2}$

∴tanθ = tan30

∴θ = 30°

$\color{red}{\bold{Ans.}}$ $\mathrm{\bold{The\: value\: of \:θ\: is \:30°.}}$