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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 (π)/(2) < α < (3π)/(4), then 2tan α + 1 cos^ 2 α is equal to

If π2<α<3π4,\dfrac{\pi}{2} < \alpha < \dfrac{3\pi}{4}, then 2tanα+1cos2α\sqrt{2tan \alpha + \dfrac{1}{cos^{2}\alpha}} is equal to

Options

  1. A−1+tanα- 1 + tan \alpha
  2. B−1−tanα- 1 - tan \alpha
  3. C1+tanα1 + tan \alpha
  4. D1−tanα1 - tan \alpha

Correct answer

B. −1−tanα- 1 - tan \alpha

Step-by-step solution

2tanα+1cos2α\sqrt{2tan \alpha + \dfrac{1}{cos^{2}\alpha}}
=2tanα+sec2α=2tanα+1+tan2α= \sqrt{2tan \alpha + sec^{2}\alpha} = \sqrt{2tan \alpha + 1 + tan^{2}\alpha}
=(1+tanα)2=∣1+tanα∣= \sqrt{{\left(1 + tan \alpha\right)}^{2}} = \left|1 + tan \alpha\right|
Since, tanα<−1tan \alpha < - 1 when π2<α<3π4\dfrac{\pi}{2} < \alpha < \dfrac{3\pi}{4}
⇒1+tanα<0⇒ 1 + tan \alpha < 0
⇒∣1+tanα∣=−1−tanα⇒ \left|1 + tan \alpha\right| = - 1 - tan \alpha
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