Paragraph: Given that x+ x+ x+ x+ x+cosec x=7 Question: If 2 x=a-b c , where a and b are natural numbers and c is prime number, then what is the value of a-b+2 c ?

Correct answer: D. 28 2 x=a-b c ^2 2 x-44 2 x+36=0 2 x= 44 ± (44)^2-4(36) 2 = 44 ± 4 11^2-9 2 =22 ± 2 112 =22 ± 8 7 2 x ≤ 1 2 x=22-8 7 =a-b c a=22, b=8, c=7a-b+2 c=22-8+14=28

NDA 2023

Exam: NDA
Year: 2023
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

NDA 2023 · Mathematics · Trigonometric Ratios & Identities

Paragraph: Given that x+ x+ x+ x+ x+cosec x=7 Question: If 2 x=a-b...

Paragraph: Given that

\sin x+\cos x+\tan x+\cot x+\sec x+\operatorname{cosec} x=7

Question: If

\sin 2 x=a-b \sqrt{c}

, where a and b are natural numbers and c is prime number, then what is the value of

\mathrm{a}-\mathrm{b}+2 \mathrm{c}

Options

A $0$
B $14$
C $21$
D $28$

Correct answer

D. $28$

Step-by-step solution

\sin 2 x=a-b \sqrt{c}\sin ^2 2 x-44 \sin 2 x+36=0\sin 2 x=\frac{44 \pm \sqrt{(44)^2-4(36)}}{2}=\frac{44 \pm 4 \sqrt{11^2-9}}{2}=22 \pm 2 \sqrt{112}=22 \pm 8 \sqrt{7}\because \quad \sin 2 x \leq 1\therefore \quad \sin 2 x=22-8 \sqrt{7}=a-b \sqrt{c}a=22, b=8, c=7a-b+2 c=22-8+14=28

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