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Let S(1) be the set of all those solutio...

Let `S_(1)` be the set of all those solution of the equation `(1+a) cos theta cos(2 theta-b)=(1+a cos 2 theta) cos (theta -b)`
which are independent of a and b and `S_(2)` be the set of all such solutions which are dependent on a and b. Then
Condition that should be imposed on a and b such that `S_(2)` in non empty is

A

`|a/2 sin b| lt 1`

B

`|a/2 sin b| le 1`

C

`|a sin b| le 1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`sin (2 theta-b)=a sin b rArr |a sin b| le 1`
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CENGAGE-TRIGONOMETRIC EQUATIONS-Exercise (Comprehension)
  1. Cosider the cubic equation : x^3-(1+costheta+sintheta)x^2+(costhetasin...

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  2. Consider the cubic equation x^3-(1+cos theta+sin theta)x^2+(cos theta ...

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  3. Consider the cubic equation x^3-(1+cos theta+sin theta)x^2+(cos theta ...

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  4. Consider the equation sec theta +cosec theta=a, theta in (0, 2pi) -{...

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  5. Consider the equation sec theta +cosec theta=a, theta in (0, 2pi) -{...

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  6. Consider the equation sec theta +cosec theta=a, theta in (0, 2pi) -{...

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  7. Consider the system of equations sin x cos 2y=(a^(2)-1)^(2)+1, cos x...

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  8. Consider the system of equations sin x cos 2y=(a^(2)-1)^(2)+1, cos x...

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  9. Consider the system of equations sin x cos 2y=(a^(2)-1)^(2)+1, cos x...

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  10. Cosider the equation int(0)^(x) (t^(2)-8t+13)dt= x sin (a//x) The nu...

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  11. Cosider the equation int(0)^(x) (t^(2)-8t+13)dt= x sin (a//x) If x t...

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  12. Cosider the equation int(0)^(x) (t^(2)-8t+13)dt= x sin (a//x) If x t...

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  13. Consider the system of equations x cos^(3) y+3x cos y sin^(2) y=14 ...

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  14. Consider the system of equations x cos^(3) y+3x cos y sin^(2) y=14 ...

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  15. Consider the system of equations x cos^(3) y+3x cos y sin^(2) y=14 ...

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  16. Let S(1) be the set of all those solution of the equation (1+a) cos th...

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  17. Let S(1) be the set of all those solution of the equation (1+a) cos th...

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  18. All the permissible value of b ,a=sin(2x-b)if a=0 and x=S(2) is a subs...

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  19. Let (b cos x)/(2 cos 2x-1)=(b + sin x)/((cos^(2) x-3 sin^(2) x) tan x)...

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  20. Let (b cos x)/(2 cos 2x-1)=(b + sin x)/((cos^(2) x-3 sin^(2) x) tan x)...

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