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JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Trigonometry

JEE Advanced · Mathematics · Trigonometry

If θ and - θ are the roots of the equation a x^2-b x-c=0 , where a,...

If sin⁡θ\sin \theta and −cos⁡θ-\cos \theta are the roots of the equation ax2−bx−c=0a x^2-b x-c=0, where a,b,ca, b, c are the sides of a triangle ABCA B C, then cos⁡B\cos B is equal to

Options

  1. A1−c2a1-\frac{c}{2 a}
  2. B1−ca1-\frac{c}{a}
  3. C1+c2a1+\frac{c}{2 a}
  4. D1+c3a1+\frac{c}{3 a}

Correct answer

C. 1+c2a1+\frac{c}{2 a}

Step-by-step solution

sin⁡θ−cos⁡θ=basin⁡θcos⁡θ=ca∴b2=a2−2ac∴cos⁡B=a2+c2−b22ac=1+c2a\begin{aligned} & \sin \theta-\cos \theta=\frac{b}{a} \\ & \sin \theta \cos \theta=\frac{c}{a} \\ & \therefore b^2=a^2-2 a c \\ & \therefore \cos B=\frac{a^2+c^2-b^2}{2 a c}=1+\frac{c}{2 a}\end{aligned}
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