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Trigonometry – II — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – II2 Marks
MCQ
$\sec50^{\circ}+\tan50^{\circ}$is equal to
  • A
    $\tan20^{\circ}+\tan50^{\circ}$
  • B
    $2\tan20^{\circ}+\tan50^{\circ}$
  • ✓
    $\tan20^{\circ}+2\tan50^{\circ}$
  • D
    $2\tan20^{\circ}+2\tan50^{\circ}$
✓

Answer

Correct option: C.
$\tan20^{\circ}+2\tan50^{\circ}$
(C)
$\sec50^{\circ}+\tan50^{\circ}$
$=\frac{1}{\cos50^{\circ}}+\tan50^{\circ}$
$=\frac{\cos20^{\circ}}{\cos20^{\circ}\cos50^{\circ}}+\tan50^{\circ}$
$=\frac{\sin70^{\circ}}{\cos20^{\circ}\cos50^{\circ}}+\tan50^{\circ}$
$\ldots\left[\because\cos\theta=\sin\left(90^{\circ}-\theta\right)\right]$
$=\frac{\sin\left(50^{\circ}+20^{\circ}\right)}{\cos20^{\circ}\cos50^{\circ}}+\tan50^{\circ}$
$=\frac{\sin50^{\circ}\cos20^{\circ}+\cos50^{\circ}\sin20^{\circ}}{\cos20^{\circ}\cos50^{\circ}}+\tan50^{\circ}$
$=\frac{\sin50^{\circ}\cos20^{\circ}}{\cos20^{\circ}\cos50^{\circ}}+\frac{\cos50^{\circ}\sin20^{\circ}}{\cos20^{\circ}\cos50^{\circ}}+\tan50^{\circ}$
$=\tan50^{\circ}+\tan20^{\circ}+\tan50^{\circ}$
$=2\tan50^{\circ}+\tan20^{\circ}$

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