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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
If $\tan A=\frac{1-\cos B}{\sin B}$, then $\tan 2 A$ is equal to
  • ✓
    $\tan B$
  • B
    $\tan ^2 B$
  • C
    $\tan ^2 B+2 \tan B$
  • D
    $\tan B+2 \tan B$
✓

Answer

Correct option: A.
$\tan B$
(A)
$\tan A =\frac{1-\cos B }{\sin B }=\frac{2 \sin ^2\left(\frac{B}{2}\right)}{2 \sin \left(\frac{B}{2}\right) \cos \left(\frac{ B }{2}\right)}=\tan \frac{ B }{2}$
$\Rightarrow \tan 2 A=\tan B$

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