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

What is the value of the following? cosec ((7 π)/(6)) ((5 π)/(3))

What is the value of the following? \operatorname{cosec} \left(\frac{7 \pi}{6}\right) \sec \left(\frac{5 \pi}{3}\right)

Options

  1. A43\frac{4}{3}
  2. B44
  3. C−4-4
  4. D−43-\frac{4}{\sqrt{3}}

Correct answer

C. −4-4

Step-by-step solution

cosec⁡(7π6)⋅sec⁡(5π3)\operatorname{cosec}\left(\frac{7 \pi}{6}\right) \cdot \sec \left(\frac{5 \pi}{3}\right)=cosec⁡(π+π6)⋅sec⁡(2π−π3)=−cosec⁡π6⋅sec⁡π3=(−2)(2)=−4\begin{aligned} & =\operatorname{cosec}\left(\pi+\frac{\pi}{6}\right) \cdot \sec \left(2 \pi-\frac{\pi}{3}\right) \\ & =-\operatorname{cosec} \frac{\pi}{6} \cdot \sec \frac{\pi}{3}=(-2)(2)=-4\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