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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2013 · Mathematics · Trigonometric Ratios & Identities

What is ^2 20^ ^ + ^2 70^ ^ equal to?

What is sin⁡220∘+sin⁡270∘\sin ^2 20^{{}^{\circ}}+\sin ^2 70^{{}^{\circ}} equal to?

Options

  1. A1
  2. B0
  3. C–1
  4. D12\frac{1}{2}

Correct answer

A. 1

Step-by-step solution

sin⁡220∘+sin⁡270∘or, sin⁡220∘+sin⁡2(90∘−20∘)or, sin⁡220∘+cos⁡2(20∘)=1.\begin{aligned} & \sin ^2 20^{{}^{\circ}}+\sin ^2 70^{{}^{\circ}} \\ & \text{or, } \sin ^2 20^{{}^{\circ}}+\sin ^2\left(90^{{}^{\circ}}-20^{{}^{\circ}}\right) \\ & \text{or, } \sin ^2 20^{{}^{\circ}}+\cos ^2\left(20^{{}^{\circ}}\right)=1.\end{aligned}
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