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Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions2 Marks
MCQ
If $(1+\tan \theta)(1+\tan \phi)=2$, then $\theta+\phi=$
  • A
    $30^{\circ}$
  • ✓
    $45^{\circ}$
  • C
    $60^{\circ}$
  • D
    $75^{\circ}$
✓

Answer

Correct option: B.
$45^{\circ}$
(B) $(1+\tan \theta)(1+\tan \phi)=2 \Rightarrow \frac{\tan \theta+\tan \phi}{1-\tan \theta \tan \phi}=1$
$\Rightarrow \tan (\theta+\phi)=1 \Rightarrow \theta+\phi=\frac{\pi}{4}=45^{\circ}$

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