Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2021 · Mathematics · Trigonometric Ratios & Identities

16. If x=-(3)/(4) and x is in the second quadrant, then what is the...

16. If tan⁡x=−34\tan x=-\frac{3}{4} and xx is in the second quadrant, then what is the value of sin⁡x⋅cos⁡x\sin x \cdot \cos x ?

Options

  1. A625\frac{6}{25}
  2. B1225\frac{12}{25}
  3. C−625-\frac{6}{25}
  4. D−1225-\frac{12}{25}

Correct answer

D. −1225-\frac{12}{25}

Step-by-step solution

tan⁡x=−34\tan x=-\frac{3}{4} ( Here 90∘<x<180∘90^{{}^{\circ}} < x < 180^{{}^{\circ}} ) sin⁡x=35\sin x=\frac{3}{5} and cos⁡x=−45\cos x=-\frac{4}{5} Now, sin⁡x⋅cos⁡x=35⋅(−45)=−1225\sin x \cdot \cos x=\frac{3}{5} \cdot\left(-\frac{4}{5}\right)=-\frac{12}{25}.
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