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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
If $\cos x=3 \cos y$, then $2 \tan \left(\frac{y-x}{2}\right)=$
  • A
    $\cot \left(\frac{y-x}{2}\right)$
  • B
    $\cot \left(\frac{x+y}{4}\right)$
  • C
    $\cot \left(\frac{y-x}{4}\right)$
  • ✓
    $\cot \left(\frac{x+y}{2}\right)$
✓

Answer

Correct option: D.
$\cot \left(\frac{x+y}{2}\right)$
(D)
$\cos x=3 \cos y \Rightarrow \frac{\cos x}{\cos y}=\frac{3}{1}$
Bt componendo and dividendo, we get $\frac{\cos x+\cos y}{\cos x-\cos y}=\frac{3+1}{3-1}$
$\Rightarrow \frac{2 \cos \left(\frac{x+y}{2}\right) \cos \left(\frac{x-y}{2}\right)}{-2 \sin \left(\frac{x+y}{2}\right) \sin \left(\frac{x-y}{2}\right)}=\frac{4}{2}$
$\Rightarrow-\cot \left(\frac{x+y}{2}\right) \cot \left(\frac{x-y}{2}\right)=2$
$\Rightarrow \cot \left(\frac{x+y}{2}\right) \cot \left(\frac{y-x}{2}\right)=2$
$\Rightarrow 2 \tan \left(\frac{y-x}{2}\right)=\cot \left(\frac{x+y}{2}\right)$

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