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Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions2 Marks
MCQ
In $\triangle ABC , \cot \frac{ A + B }{2} \cdot \tan \frac{A- B }{2}=$
  • A
    $\frac{a+b}{a-b}$
  • ✓
    $\frac{a-b}{a+b}$
  • C
    $\frac{a}{a+b}$
  • D
    $\frac{b}{a+b}$
✓

Answer

Correct option: B.
$\frac{a-b}{a+b}$
(B) $\tan \frac{A-B}{2}=\frac{a-b}{a+b} \cot \frac{C}{2}$
$=\frac{ a - b }{ a + b } \tan \left(\frac{ A + B }{2}\right)$ $\ldots[\because A+B+C=\pi]$
$\therefore \quad \tan \frac{A-B}{2} \cot \frac{A+B}{2}=\frac{a-b}{a+b}$

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