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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2021 · Mathematics · Trigonometric Ratios & Identities

What is the value of the following? 31^ ^ 33^ ^ 35^ ^ ________ 57^...

What is the value of the following? \tan 31^{{}^{\circ}} \tan 33^{{}^{\circ}} \tan 35^{{}^{\circ}} ________ \tan 57^{{}^{\circ}} \tan 59^{{}^{\circ}}

Options

  1. A−1-1
  2. B00
  3. C11
  4. D22

Correct answer

C. 11

Step-by-step solution

tan⁡31∘⋅tan⁡33∘⋅tan⁡35∘………tan⁡55∘⋅tan⁡57∘⋅tan⁡59∘=tan⁡31∘⋅tan⁡33∘⋅tan⁡35∘………\begin{aligned} & \tan 31^{{}^{\circ}} \cdot \tan 33^{{}^{\circ}} \cdot \tan 35^{{}^{\circ}} \ldots \ldots \ldots \tan 55^{{}^{\circ}} \cdot \tan 57^{{}^{\circ}} \cdot \tan 59^{{}^{\circ}} \\ & =\tan 31^{{}^{\circ}} \cdot \tan 33^{{}^{\circ}} \cdot \tan 35^{{}^{\circ}} \ldots \ldots \ldots\end{aligned}tan⁡(90∘−35∘)⋅tan⁡(90∘−33∘)⋅tan⁡(90∘−31∘)=tan⁡31∘⋅tan⁡33∘⋅tan⁡35∘………tan⁡45∘………..\begin{aligned} & \tan \left(90^{{}^{\circ}}-35^{{}^{\circ}}\right) \cdot \tan \left(90^{{}^{\circ}}-33^{{}^{\circ}}\right) \cdot \tan \left(90^{{}^{\circ}}-31^{{}^{\circ}}\right) \\ & =\tan 31^{{}^{\circ}} \cdot \tan 33^{{}^{\circ}} \cdot \tan 35^{{}^{\circ}} \ldots \ldots \ldots \tan 45^{{}^{\circ}} \ldots \ldots \ldots..\end{aligned}\cot 35^{{}^{\circ}} \cdot \cot 33^{{}^{\circ}} \cdot \cot 31^{{}^{\circ}}=1$.
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