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

NDA 2013 · Mathematics · Trigonometric Ratios & Identities

What is 54^ ^ 36^ ^ + 20^ ^ 70^ ^ equal to?

What is \frac{\cos 54^{{}^{\circ}}}{\tan 36^{{}^{\circ}}}+\frac{\tan 20^{{}^{\circ}}}{\cot 70^{{}^{\circ}}}$ equal to?

Options

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

Correct answer

C. 2

Step-by-step solution

cot⁡54∘tan⁡36∘+tan⁡20∘cot⁡70∘tan⁡(90∘−54∘)tan⁡36∘+tan⁡20∘tan⁡(90∘−70∘)tan⁡36∘tan⁡36∘+tan⁡20∘tan⁡20∘=1+1=2\begin{aligned} & \frac{\cot 54^{{}^{\circ}}}{\tan 36^{{}^{\circ}}}+\frac{\tan 20^{{}^{\circ}}}{\cot 70^{{}^{\circ}}} \\ & \frac{\tan \left(90^{{}^{\circ}}-54^{{}^{\circ}}\right)}{\tan 36^{{}^{\circ}}}+\frac{\tan 20^{{}^{\circ}}}{\tan \left(90^{{}^{\circ}}-70^{{}^{\circ}}\right)} \\ & \frac{\tan 36^{{}^{\circ}}}{\tan 36^{{}^{\circ}}}+\frac{\tan 20^{{}^{\circ}}}{\tan 20^{{}^{\circ}}}=1+1=2\end{aligned}
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