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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
$\tan \left(\frac{\pi}{4}+\frac{\theta}{2}\right)+\tan \left(\frac{\pi}{4}-\frac{\theta}{2}\right)$ is equal to
  • A
    $\sec \theta$
  • ✓
    $2 \sec \theta$
  • C
    $\sec \frac{\theta}{2}$
  • D
    $\sin \theta$
✓

Answer

Correct option: B.
$2 \sec \theta$
(B)
$\tan \left(\frac{\pi}{4}+\frac{\theta}{2}\right)+\tan \left(\frac{\pi}{4}-\frac{\theta}{2}\right)$
$=\frac{1+\tan \frac{\theta}{2}}{1-\tan \frac{\theta}{2}}+\frac{1-\tan \frac{\theta}{2}}{1+\tan \frac{\theta}{2}}$
$=\frac{\left(1+\tan \frac{\theta}{2}\right)^2+\left(1-\tan \frac{\theta}{2}\right)^2}{1-\tan ^2 \frac{\theta}{2}}$
$=2\left(\frac{1+\tan ^2 \frac{\theta}{2}}{1-\tan ^2 \frac{\theta}{2}}\right)$
$=\frac{2}{\cos \theta}$
$=2 \sec \theta$

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