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Let 0<theta1<theta2<theta3< denote the p...

Let `0

A

`6pi`

B

`7pi`

C

`8pi`

D

`4pi`

Text Solution

Verified by Experts

The correct Answer is:
A
`3+3 cos theta =2 -2 cos^(2) theta`
`rArr 2 cos^(2) theta+3 cos theta+1=0`
`rArr (2 cos theta+1) (cos theta+1) =0`
`:. Cos theta=-1 or cos theta=-1/2`
If `cos theta=-1` then `theta=pi, 3 pi, 5 pi, 7 pi, 9pi`, ...
If `cos theta=-1//2` then `theta=(2pi)/3, (4pi)/3, (8pi)/3, (10 pi)/3, (14 pi)/3, ...`
Solution in increasing order are
`(2pi)/3 lt pi lt (4pi)/3 lt (8 pi)/3 lt 3pi lt (10 pi)/3 lt (14 pi)/3 lt 5pi`, ...
`:. theta_(3)+theta_(7)=(4pi)/3+(14 pi)/3=6pi`
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CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Single)
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  8. The number of solutions of 12 cos^(3) x-7 cos^(2) x+4 cos x=9 is

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  10. The general solution of (tan 5x-tan 4x)/(1+ tan 5 x tan 4x)=1 is

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  11. If xsina+ysin2a+zsin3a=sin4a xsinb+ysin2b+zsin3b=sin4b xsinc+ysin2c+...

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  12. The number of solutions of the equation sin 2 theta-2 cos theta +4 sin...

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  13. The number of distinct real roots of the equation tan(2pix)/(x^2+x+1)=...

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  14. The smallest positive value of x (in radians) satisfying the equation ...

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  15. The number of solution of sin^(4)x-cos^(2) x sin x+2 sin^(2)x+sin x=0 ...

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  16. The range of 'y, such that the equation in x, y + cos x = sin x has a ...

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  17. Solution of the equation sin (sqrt(1+sin 2 theta))= sin theta + cos th...

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  18. One of the general solutions of sqrt(3) cos theta -3 sin theta =4 sin ...

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  19. The general solution of the equation 8 cos x cos 2x cos 4x = sin 6x//s...

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  20. (sin^(3) theta-cos^(3) theta)/(sin theta - cos theta)- (cos theta)/sqr...

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