Trigonometrical Equations 1 Question 21

21. Let a,b,c be three non-zero real numbers such that the equation 3acosx+2bsinx=c,xπ2,π2, has two distinct real roots α and β with α+β=π3. Then, the value of ba is

(2018 Adv.)

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Answer:

Correct Answer: 21. (0.5)

Solution:

  1. We have, α,β are the roots of

3acosx+2bsinx=c3acosα+2bsinα=c and 3acosβ+2bsinβ=c

On subtracting Eq. (ii) from Eq. (i), we get

3a(cosαcosβ)+2b(sinαsinβ)=0

3a2sinα+β2sinαβ2

+2b2cosα+β2sinαβ2=0

3asinα+β2=2bcosα+β2

tanα+β2=2b3a

tanπ6=2b3aα+β=π3, given

13=2b3aba=12

ba=0.5



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