Question

FIND THE VALUE OF-:

$\begin{gathered} \ \: \\ \frac{2cos^245° + 3 \tan^230°}{ \sqrt{3 \cos(30°) \sin(30°) } } \end{gathered}$ ​ ​ ━━━━━━━━━━━━━━━━━━━━━━
➦TOPIC - TRIGONOMETRY

➦CLASS - 10 th

➦NO SPAM ​

Answer 1

Lets do

$\\ \sf\longmapsto \frac{2 { \cos }^{2}45 + 3 {tan}^{2}30 }{ \sqrt{3 \cos(30) \sin(30) } } \\ \\ \sf\longmapsto \frac{2 \left( \frac{1}{ \sqrt{2} } \right) {}^{2} + 3 \left( \frac{1}{ \sqrt{3} } \right) {}^{2} }{ \sqrt{3 \times \frac{ \sqrt{3} }{2} \times \frac{1}{2} }} \\ \\ \sf\longmapsto \frac{ 2 \times \frac{1}{2} + 3 \times \frac{1}{3} }{ \sqrt{ \frac{3 \sqrt{3} }{4} }} \\ \\ \sf\longmapsto \frac{1 + 1}{ \frac{3 \sqrt{3} }{2} } \\ \\ \sf\longmapsto \frac{2}{ \frac{3 \sqrt{3} }{2} } \\ \\ \sf\longmapsto \frac{2 \times 2}{3 \sqrt{3} } \\ \\ \sf\longmapsto \frac{4}{3 \sqrt{3} }$