Question

a of tan theta = 2-√3, then prove
that cot theta =2+√3.​

Answer 1

Need to FinD :-

• The value of cot theta .

$\red{\frak{Given}}\Bigg\{\sf tan\theta = 2-\sqrt3$

Given that the value of tanθ = 2 - √3 . We need to find out the value of cotθ . We know that ,

$\sf\longrightarrow tan\theta =\dfrac{1}{cot\theta}$

Therefore ,

$\sf\longrightarrow cot\theta =\dfrac{1}{tan\theta}$

Put on the Value of tanθ ,

$\sf\longrightarrow cot\theta =\dfrac{1}{tan\theta} \\\\\\\sf\longrightarrow cot\theta =\dfrac{1}{2-\sqrt3}$

Rationalise the denominator ,

$\sf\longrightarrow cot\theta =\dfrac{1(2+\sqrt3)}{(2-\sqrt3)(2+\sqrt3)}\\\\\\\sf\longrightarrow cot\theta = \dfrac{2+\sqrt{3}}{(2)^2-(\sqrt3)^2}\\\\\\\sf\longrightarrow cot\theta = \dfrac{2+\sqrt{3}}{4-3} \\\\\\\sf\longrightarrow \underline{\underline{\red{cot\theta = 2+\sqrt3}}}$