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

JEE Main · Mathematics · Trigonometric Ratios & Identities

12^ ^ ^ - 12^ ^ ^ 12^ ^ ^ + 12^ ^ ^ + 147^ ^ ^ 147^ ^ ^ =

cos⁡12∘−sin⁡12∘cos⁡12∘+sin⁡12∘+sin⁡147∘cos⁡147∘=\frac{\cos 12^{{}^{{}^{\circ}}}-\sin 12^{{}^{{}^{\circ}}}}{\cos 12^{{}^{{}^{\circ}}}+\sin 12^{{}^{{}^{\circ}}}}+\frac{\sin 147^{{}^{{}^{\circ}}}}{\cos 147^{{}^{{}^{\circ}}}}=

Options

  1. A-2
  2. B0
  3. C-1
  4. D1

Correct answer

B. 0

Step-by-step solution

\cos 12^{{}^{{}^{\circ}}}-\cos 78^{{}^{{}^{\circ}}}}{\cos 12^{{}^{{}^{\circ}}}+\cos 78^{{}^{{}^{\circ}}}}+\tan 147^{{}^{{}^{\circ}}}=\frac{-2 \sin 45^{{}^{{}^{\circ}}} \sin \left(-33^{{}^{{}^{\circ}}}\right)}{2 \cos 45^{{}^{{}^{\circ}}} \cos 33^{{}^{{}^{\circ}}}}+\tan \left(180^{{}^{{}^{\circ}}}-33^{{}^{{}^{\circ}}}\right)=\tan 45^{{}^{{}^{\circ}}} \tan 33^{{}^{{}^{\circ}}}-\tan 33^{{}^{{}^{\circ}}}=\tan 33^{{}^{{}^{\circ}}}-\tan 33^{{}^{{}^{\circ}}}=0
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