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Introduction of Trigonometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry1 Mark
MCQ
$\tan10^\circ\tan15^\circ\tan75^\circ\tan80^\circ=?$
  • A
    $\sqrt{3}$
  • B
    $\frac{1}{\sqrt{3}}$
  • C
    $-1$
  • ✓
    $1$
✓

Answer

Correct option: D.
$1$
$\tan10^\circ\tan15^\circ\tan75^\circ\tan80^\circ$
$=\tan10^\circ\tan15^\circ\tan(90^\circ-15^\circ)\tan(90^\circ-10^\circ)$
$=\tan10^\circ\tan15^\circ\cot15^\circ\cot10^\circ$
$=(\tan10^\circ\cot10^\circ)(\tan15^\circ\cot15^\circ)$
$=1\times1$
$=1$

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