22 b. Evaluate: (2 cos 30 – cot ^3 60)/tan 30

Question

Q) Evaluate: $\frac{2 \cos 30^\circ - \cot^3 60^\circ}{	an 30^\circ}$.
(Q 22 B - 30/5/2 - CBSE 2026 Question Paper)

Sapling Academy · Accepted Answer

We know that cos 30 0 = $\frac{\sqrt 3}{2}$
cot 60 0 = $\frac{1}{\sqrt 3}$
and tan 30 0 = $\frac{1}{\sqrt 3}$
Given expression is: $\frac{2 \cos 30^\circ - \cot^3 60^\circ}{	an 30^\circ}$
By substituting these values, we get:
= $\frac{(2 (\cos 30^\circ) - (\cot 60^\circ)^3)}{(	an 30^\circ)}$
= $\frac{2 (\frac{\sqrt 3}{2}) - (\frac{1}{\sqrt 3})^3}{\frac{1}{\sqrt 3}}$ 
= $\frac{(\sqrt 3) - (\frac{1}{3\sqrt 3})}{\frac{1}{\sqrt 3}}$
= $\frac{(9 - 1)}{3\sqrt 3} 	imes {\frac{\sqrt 3}{1}}$
= $\frac{8\sqrt 3}{3\sqrt 3}$ = $\frac{8}{3}$
Therefore, the value of the given expression is $\frac{8}{3}$.
Please press "Heart" if you liked the solution.

Leave a Comment Cancel Reply

Contact us

Join us

Useful Link

Our Quizzes

Related Math Questions

Leave a Comment Cancel Reply