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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(3 π)+ ^2(4 π)+ ^2(5 π) equal to?

What is sin⁡2(3π)+cos⁡2(4π)+tan⁡2(5π)\sin ^2(3 \pi)+\cos ^2(4 \pi)+\tan ^2(5 \pi) equal to?

Options

  1. A0
  2. B1
  3. C2
  4. D3

Correct answer

B. 1

Step-by-step solution

sin⁡2(3π)+cos⁡2(4π)+tan⁡2(5π)=(0)2+(1)2+sin⁡2(5π)cos⁡2(5π)=0+1+0=1[∵sin⁡nπ=0cos⁡nπ=(−1)n]\begin{aligned} & \sin ^2(3 \pi)+\cos ^2(4 \pi)+\tan ^2(5 \pi) \\ & =(0)^2+(1)^2+\frac{\sin ^2(5 \pi)}{\cos ^2(5 \pi)} \\ & =0+1+0=1 \quad\left[\begin{array}{l} \because \sin n \pi=0 \\ \cos n \pi=(-1)^n \end{array}\right] \end{aligned}
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