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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
$\tan100^{\circ}+\tan125^{\circ}+\tan100^{\circ}\tan125^{\circ}=$
  • A
    $0$
  • B
    $\frac{1}{2}$
  • C
    -1
  • ✓
    1
✓

Answer

Correct option: D.
1
(D)
$\tan\left(100^{\circ}+125^{\circ}\right)=\frac{\tan100^{\circ}+\tan125^{\circ}}{1-\tan100^{\circ}\tan125^{\circ}}$
$\Rightarrow\tan225^{\circ}=\frac{\tan100^{\circ}+\tan125^{\circ}}{1-\tan100^{\circ}\tan125^{\circ}}$
$\Rightarrow1=\frac{\tan100^{\circ}+\tan125^{\circ}}{1-\tan100^{\circ}\tan125^{\circ}}$
$\Rightarrow1=\frac{\tan100^{\circ}+\tan125^{\circ}}{1-\tan100^{\circ}\tan125^{\circ}}$
$\ldots\left[\because\tan\left(180^{\circ}+45^{\circ}\right)=\tan45^{\circ}=1\right]$
$\Rightarrow\tan100^{\circ}+\tan125^{\circ}+\tan100^{\circ}\tan125^{\circ}=1$

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