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If alpha a n d beta are the solutions of...

If `alpha a n d beta` are the solutions of the equation `at a ntheta+bs e ctheta=c ,` then show that `tan(alpha+beta)=(2a c)/(a^2-c^2)`

A

`(2ac)/(a^(2) -c^(2))`

B

`(2ac)/(c^(2) -a^(2))`

C

`(2ac)/(a^(2) +c^(2))`

D

`(ac)/(a^(2) +c^(2))`

Text Solution

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The correct Answer is:
A
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OBJECTIVE RD SHARMA ENGLISH-TRIGONOMETRIC EQUATIONS AND INEQUATIONS-Exercise
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  2. If 1+sintheta+sin^2theta+sin^3theta+..to oo=4+2sqrt3 0<theta<pi, t...

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  3. If alpha a n d beta are the solutions of the equation at a ntheta+bs e...

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  4. Solve sinx+siny=sin(x+y)a n d|x|+|y|=1

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  5. The expression (1 + tan x + tan^2 x)(1-cot x + cot^2 x) has the positi...

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  6. If the the equation a sin x + cos 2x=2a-7 possesses a solution, then f...

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  7. The equation "sin"^(6) x + "cos"^(6) x = lambda, has a solution if

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  8. If y + "cos" theta = "sin" theta has a real solution, then

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  9. The solution set of the equation 4 sin theta. Cos theta-2 cos theta-2s...

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  10. The most general solution of tan theta =-1 and cos theta = 1/(sqrt(2))...

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  11. The complex numbers sin x +i cos 2x and cos x -i sin 2x are conjugate ...

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  12. The smallest positive root of the equation tanx-x=0 lies in (0,pi/2) ...

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  13. The number of solutions of the equation "sin" x = "cos" 3x " in " [0, ...

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  14. Find the general values of theta satisfying tan theta + tan ((3pi)/...

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  15. If sin theta+ cos theta = sqrt(2) cos theta, (theta ne 90^(@)) then v...

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  16. The number of solutions of the equation tanx+secx=2cosx lying in the i...

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  17. If "cot" theta "cot" 7 theta + "cot" theta "cot" 4 theta + "cot" 4 the...

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  18. Find the number of value of x in [0,5pi] satisying the equation 3 cos...

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  19. The number of values of x in [0, 2 pi] that satisfy "cot" x -"cosec"x ...

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  20. "cot" theta = "sin" 2 theta, theta ne n pi, n in Z, "if" theta equals

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