Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2017 · Mathematics · Trigonometric Ratios & Identities

If (α+β)=2 and (α-β)=1 , then (2 α) is equal to

If tan⁡(α+β)=2\tan (\alpha+\beta)=2 and tan⁡(α−β)=1\tan (\alpha-\beta)=1, then tan⁡(2α)\tan (2 \alpha) is equal to

Options

  1. A-3
  2. B-2
  3. C-1/3
  4. D1

Correct answer

A. -3

Step-by-step solution

tan⁡(α+β)=2tan⁡(α−β)=1tan⁡2α=tan⁡[(α+β)+(α−β)]=tan⁡(α+β)+tan⁡(α−β)1−tan⁡(α+β)⋅tan⁡(α−β)=2+11−2.1=3−1=−3\begin{aligned} & \tan (\alpha+\beta)=2 \\ & \tan (\alpha-\beta)=1 \\ & \tan 2 \alpha=\tan [(\alpha+\beta)+(\alpha-\beta)] \\ & =\frac{\tan (\alpha+\beta)+\tan (\alpha-\beta)}{1-\tan (\alpha+\beta) \cdot \tan (\alpha-\beta)} \\ & =\frac{2+1}{1-2.1}=\frac{3}{-1}=-3\end{aligned}
Practice Trigonometric Ratios & Identities on Quantrex Academy →

More from Trigonometric Ratios & Identities

If θ lies in the fourth quadrant and 3 θ+4=0 , then what is the value of 2θ+ 2θ ? NDA 2026If α+ β=0= α+ β , α≠β then what is a value of 2α+ 2β+2 (α+β) ? NDA 2026If 2 4β= 2α+ 2α , then which one of the following is a possible value of (α+β) ? NDA 2026If x= θ- θ and y= θ+ θ , then which one of the following is correct ? NDA 2026If θ=(1)/(3) , then what is the value of ((θ)/(2)) ((3θ)/(2)) ? NDA 2026If A and B are acute angles such that 2A+2B=π , then what is the maximum value of A· B ? NDA 2026x+ 3 x is maximum when x is equal to NDA 2026In a triangle ABC , A= B+ C then what is ((B)/(2))+ ((B)/(2))equal to ? NDA 2026If α and β are complementary angles such that α-β=(π)/(6) and m β=n α , then what is… NDA 2026For the following two (02) items: Let A + B = p and A + B = q . What is (p^2 - q^2)/(p^2… NDA 2025For the following two (02) items: Let p = cosec\, 20° and q = cosec\, 70° . What is (p^2… NDA 2025For the following two (02) items: Let A + B = p and A + B = q . What is (p)/(q) equal to? NDA 2025For the following two (02) items: Let p = cosec\, 20° and q = cosec\, 70° . What is ( 3… NDA 2025Consider the following for the three (03) items that follow: Let p = 35° , q = 25° and r… NDA 2025Consider the following for the three (03) items that follow: Let p = 35° , q = 25° and r… NDA 2025Consider the following for the three (03) items that follow: Let p = 35° , q = 25° and r… NDA 2025 Full Trigonometric Ratios & Identities list Trigonometric Ratios & Identities JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs