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JEE Main 202225 JuneEvening Shift
Exam
JEE Main
Year
2022
Date
25 June
Shift
Evening Shift
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

JEE Main 2022 · 25 June · Evening Shift · Mathematics · Trigonometric Ratios & Identities

The value of 2 12 ° - 72 ° is

The value of 2sin⁡12°−sin⁡72°2\sin 12 ° - \sin 72 ° is

Options

  1. A\dfrac{\sqrt{5}\left(1 - \sqrt{3}\right)}{4}
  2. B1−58\dfrac{1 - \sqrt{5}}{8}
  3. C\dfrac{\sqrt{3}\left(1 - \sqrt{5}\right)}{2}
  4. D\dfrac{\sqrt{3}\left(1 - \sqrt{5}\right)}{4}

Correct answer

D. \dfrac{\sqrt{3}\left(1 - \sqrt{5}\right)}{4}

Step-by-step solution

To find ⇒2sin⁡12°−sin⁡72⇒ 2\sin 12 ° - \sin 72

⇒sin⁡12°+sin⁡12°−sin⁡72⇒ \sin 12 ° + \sin 12 ° - \sin 72

⇒sin⁡12°+2cos⁡42°sin⁡(−30°)⇒ \sin 12 ° + 2\cos 42 ° \sin \left(- 30 °\right)⇒ \sin 12 ° - \cos 42 °<br/><br/><br /><br />⇒ \sin 12 ° - \sin 48 ° ⇒ 2\cos \left(30 °\right)\sin \left(- 18 °\right)</p><p></p><p>⇒ - \sqrt{3}\sin 18 ° = - \sqrt{3}\left(\dfrac{\sqrt{5} - 1}{4}\right)=3(1−54)= \sqrt{3}\left(\dfrac{1 - \sqrt{5}}{4}\right)

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