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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NTA Abhyas 2020 · Mathematics · Trigonometric Ratios & Identities

If tan 25 ^ o = a, then the value of tan 205 ^ o - tan 115 ^ o tan...

If tan25o=a,tan{25}^{o} = a, then the value of tan205o−tan115otan245o+tan335o\dfrac{tan {205}^{o} - tan {115}^{o}}{tan {245}^{o} + tan {335}^{o}} in terms of aa& is

Options

  1. A1−a21+a2\dfrac{1 - a^{2}}{1 + a^{2}}
  2. B1−a2a\dfrac{1 - a}{2a}
  3. C2a1+a2\dfrac{2a}{1 + a^{2}}
  4. D1+a21−a2\dfrac{1 + a^{2}}{1 - a^{2}}

Correct answer

D. 1+a21−a2\dfrac{1 + a^{2}}{1 - a^{2}}

Step-by-step solution

tan205o−tan115otan245o+tan335o=tan25o+cot25ocot25o−tan25o\dfrac{tan {205}^{o} - tan {115}^{o}}{tan {245}^{o} + tan {335}^{o}} = \dfrac{tan {25}^{o} + cot {25}^{o}}{cot {25}^{o} - tan {25}^{o}}
=tan⁡225o+11−tan⁡225o=a2+11−a2= \dfrac{\tan^{2} {25}^{o} + 1}{1 - \tan^{2} {25}^{o}} = \dfrac{a^{2} + 1}{1 - a^{2}}
=1+a21−a2= \dfrac{1 + a^{2}}{1 - a^{2}}
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