Evaluate : 5 tan 60° / (sin2 60° + cos2 60°) tan 30°

Q) Evaluate : 5 tan 60° / (sin2 60° + cos2 60°) tan 30°

Ans:

We know that: tan 60⁰ = √ 3, sin 60 ⁰ = $\frac{\sqrt 3}{2}$ , cos 60⁰ = $\frac{1}{2}$ ; tan 30⁰ = $\frac{1}{\sqrt 3}$ ;

By submitting these values in the given expression, we get:

$\frac{5 tan 60}{(sin^2 60 + cos^2 60) tan 30}$

$\frac{5 (\sqrt 3)}{[(\frac{\sqrt 3}{2})^2 + (\frac{1}{2})^2](\frac{1}{\sqrt 3})}$

= $\frac{5 (\sqrt 3)}{[(\frac{3}{4})+ (\frac{1}{4})](\frac{1}{\sqrt 3})}$

= $\frac{5 (\sqrt 3)}{[(1)](\frac{1}{\sqrt 3})}$ = 5 √3 x √3

= 5 x 3 = 15

Hence the value of the given function is 15.

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