Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2019 · Mathematics · Trigonometric Ratios & Identities

What is ((A)/(2))- ((A)/(2))equal to?

What is cot⁡(A2)−tan⁡(A2)equalto?\cot \left(\frac{A}{2}\right)-\tan \left(\frac{A}{2}\right)equal to?

Options

  1. Atan⁡A\tan \mathrm{A}
  2. Bcot⁡A\cot \mathrm{A}
  3. C2tan⁡A2 \tan \mathrm{ A}
  4. D2cot⁡A2 \cot \mathrm{ A}

Correct answer

D. 2cot⁡A2 \cot \mathrm{ A}

Step-by-step solution

cot⁡A2−tan⁡A2=cos⁡A2sin⁡A2−sin⁡A2cos⁡A2=cos⁡2A2−sin⁡2A2sin⁡A2⋅cos⁡A2×22=2⋅cos⁡Asin⁡A=2cot⁡A\begin{aligned} & \cot \frac{A}{2}-\tan \frac{A}{2} \\ & =\frac{\cos \frac{A}{2}}{\sin \frac{A}{2}}-\frac{\sin \frac{A}{2}}{\cos \frac{A}{2}} \\ & =\frac{\cos ^2 \frac{A}{2}-\sin ^2 \frac{A}{2}}{\sin \frac{A}{2} \cdot \cos \frac{A}{2}} \times \frac{2}{2} \\ & =2 \cdot \frac{\cos A}{\sin A}=2 \cot A \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