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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

JEE Main · Mathematics · Trigonometric Ratios & Identities

1 - 2[cos 60 ^ o - cos 80 ^ o ] 2sin 10 ^ o = ….

1−2[cos60o−cos80o]2sin10o=\dfrac{1 - 2\left[cos{60}^{o} - cos{80}^{o}\right]}{2sin{10}^{o}} = ….

Options

  1. A2
  2. B1
  3. C12\dfrac{1}{2}
  4. D32\dfrac{3}{2}

Correct answer

B. 1

Step-by-step solution

We have, \dfrac{1 - 2\left(\text{ cos }{60}^{o} -\text{ cos }{80}^{o}\right)}{2sin{10}^{o}}<br/><br/>= \dfrac{1 - 2\left(\dfrac{1}{2} - cos{80}^{o}\right)}{2sin{10}^{o}}
=2cos80o2sin10o= \dfrac{2cos{80}^{o}}{2sin{10}^{o}}
= \dfrac{\cos \left({90}^{o} - {10}^{o}\right)}{sin{10}^{o}}<br/><br/>= \dfrac{sin{10}^{o}}{sin{10}^{o}} = 1
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