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Introduction of Trigonometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry1 Mark
MCQ
$\frac{2\tan^230^\circ\sec^252^\circ\sin^238^\circ}{\text{cosec}^270^\circ-\tan^220^\circ}=?$
  • A
    $2$
  • B
    $\frac{1}{2}$
  • ✓
    $\frac{2}{3}$
  • D
    $\frac{3}{2}$
✓

Answer

Correct option: C.
$\frac{2}{3}$
$\frac{2\tan^230^\circ\sec^252^\circ\sin^238^\circ}{\text{cosec}^270^\circ-\tan^220^\circ}$
$=\frac{2\times\big(\frac{1}{\sqrt3}\big)^2\times\frac{1}{\cos^252^\circ}\times\sin^2(90^\circ-52^\circ)}{\text{cosec}^2(90^\circ-20^\circ)-\tan^220^\circ}$
$=\frac{2\times\frac{1}{3}\times\frac{1}{\cos^252^\circ}\times\cos^252^\circ}{\sec^220^\circ-\tan^220^\circ}$
$=\frac{\frac{2}{3}}1{}$
$=\frac{2}{3}$

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