Evaluate \(\frac{2\sin 30 + 5\tan 60}{\sin 60}\), leaving your answer in surd form.

  • A \(\frac{2\sqrt{3}}{3} + 10\)
  • B \(\frac{3\sqrt{2} - 1}{5}\)
  • C \(\frac{3\sqrt{2} + 1}{5}\)
  • D \(\frac{2\sqrt{3}}{3} - 10\)
jamb 2019mathematics

The correct answer is A. \(\frac{2\sqrt{3}}{3} + 10\)

The given expression is \(\frac{2\sin 30 + 5\tan 60}{\sin 60}\).

We know that:
- \(\sin 30 = \frac{1}{2}\)
- \(\tan 60 = \sqrt{3}\)
- \(\sin 60 = \frac{\sqrt{3}}{2}\)

Substituting these values into the expression gives:

\(\frac{2\sin 30 + 5\tan 60}{\sin 60} = \frac{2*\frac{1}{2} + 5*\sqrt{3}}{\frac{\sqrt{3}}{2}} = \frac{1 + 5\sqrt{3}}{\frac{\sqrt{3}}{2}} = \frac{2(1 + 5\sqrt{3})}{\sqrt{3}} = \frac{2 + 10\sqrt{3}}{\sqrt{3}} = 2\sqrt{3} + 10\)

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