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Introduction of Trigonometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry1 Mark
MCQ
Choose the correct option and justify your choice : $\frac{2\tan30^\circ}{1+\tan^230^\circ}=$
  • ✓
    $\sin 60^\circ$
  • B
    $\cos 60^\circ$
  • C
    $\tan 60^\circ$
  • D
    $\sin 30^\circ$
✓

Answer

Correct option: A.
$\sin 60^\circ$
$\frac{2\tan30^\circ}{1+\tan^230^\circ}=\frac{2\times\frac{1}{\sqrt{3}}}{1+\Big(\frac{1}{\sqrt{3}}\Big)^2}=\frac{\frac{2}{\sqrt{3}}}{1+\frac{1}{3}} $
$=\frac{\frac{2}{\sqrt{3}}\times3}{4} $
$ =\frac{{2}{\sqrt{3}}}{4}=\frac{\sqrt{3}}{2}$
$=\sin 60^\circ $

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