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NDA 2014
Exam
NDA
Year
2014
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2014 · Mathematics · Trigonometric Ratios & Identities

What is ^2 66 (1)/(2)^ ^ - ^2 23 (1)/(2)^ ^ equal to?

What is sin⁡26612∘−sin⁡22312∘\sin ^2 66 \frac{1}{2}^{{}^{\circ}}-\sin ^2 23 \frac{1}{2}^{{}^{\circ}} equal to?

Options

  1. Asin⁡47∘\sin 47^{{}^{\circ}}
  2. Bcos⁡47∘\cos 47^{{}^{\circ}}
  3. C2sin⁡47∘2 \sin 47^{{}^{\circ}}
  4. D2cos⁡47∘2 \cos 47^{{}^{\circ}}

Correct answer

B. cos⁡47∘\cos 47^{{}^{\circ}}

Step-by-step solution

sin⁡90∘⋅sin⁡(43∘)=sin⁡(90∘−47∘)=cos⁡47∘\sin 90^{{}^{\circ}} \cdot \sin \left(43^{{}^{\circ}}\right)=\sin \left(90^{{}^{\circ}}-47^{{}^{\circ}}\right)=\cos 47^{{}^{\circ}}
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