Question

find the value of tan² 60⁰+cot³ 30⁰/sin² 30⁰+cos² 60⁰ in teeth

Answer 1

Answer:

The answer is $\frac{18\sqrt 3+2}{3\sqrt 3}$

Step-by-step explanation:

Since we know that

$\tan60^\circ=\sqrt 3,\cot 30^\circ=\frac{1}{\sqrt 3},\sin 30^\circ=\frac{1}{2}, \cos 60^\circ=\frac{1}{2}$

Therefore

$\frac{\tan^260^\circ+\cot^ 330^\circ}{\sin^230^\circ+\cos^260^\circ} =\frac{(\sqrt 3)^2+(\frac{1}{\sqrt 3})^3}{\frac{1}{4}+\frac{1}{4}}=\frac{3+\frac{1}{3\sqrt 3}}{\frac{1}{2}}\\=\frac{\frac{9\sqrt 3+1}{3\sqrt3}}{\frac{1}{2}}=\frac{18\sqrt 3+2}{3\sqrt 3}$