Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2020 · Mathematics · Trigonometric Ratios & Identities

Paragraph: Read the following information and answer Let t_n= ^n θ+...

Paragraph: Read the following information and answer Let tn=sin⁡nθ+cos⁡nθt_n=\sin ^n \theta+\cos ^n \theta.
Question: What is t12−t2t_1^2-t_2 equal to?

Options

  1. Acos⁡2θ\cos 2 \theta
  2. Bsin⁡2θ\sin 2 \theta
  3. C2cos⁡θ2 \cos \theta
  4. D2sin⁡θ2 \sin \theta

Correct answer

B. sin⁡2θ\sin 2 \theta

Step-by-step solution

t12−t2=(sin⁡θ+cos⁡θ)2−(sin⁡2θ+cos⁡2θ)=sin⁡2θ+cos⁡2θ+2sin⁡θ⋅cos⁡θ−(sin⁡2θ+cos⁡2θ)=1+sin⁡2θ−1=sin⁡2θ\begin{aligned} & t_1^2-t_2=(\sin \theta+\cos \theta)^2-\left(\sin ^2 \theta+\cos ^2 \theta\right) \\ = & \sin ^2 \theta+\cos ^2 \theta+2 \sin \theta \cdot \cos \theta-\left(\sin ^2 \theta+\cos ^2 \theta\right) \\ = & 1+\sin 2 \theta-1=\sin 2 \theta\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