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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
If $\tan A -\tan B =x$ and $\cot B -\cot A =y$, then $\cot (A-B)=$
  • A
    $\frac{1}{x}+y$
  • B
    $\frac{1}{x y}$
  • C
    $\frac{1}{x}-\frac{1}{y}$
  • ✓
    $\frac{1}{x}+\frac{1}{y}$
✓

Answer

Correct option: D.
$\frac{1}{x}+\frac{1}{y}$
(D)
$\cot (A-B)=\frac{1}{\tan (A-B)}$
$=\frac{1+\tan A \tan B}{\tan A-\tan B}$
$=\frac{1}{\tan A-\tan B}+\frac{\tan A \tan B}{\tan A-\tan B}$
$=\frac{1}{\tan A-\tan B}+\frac{1}{\cot B-\cot A}$
$=\frac{1}{x}+\frac{1}{y}$

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