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Prove that: tan^-1((c1x-y)/(c1y+x))+tan^...

Prove that: `tan^-1((c_1x-y)/(c_1y+x))+tan^-1((c_2-c_1)/(1+c_2c_1))+tan^-1((c_3-c_2)/(1+c_3c_2))` +`.......+tan^-1((c_n-c_(n-1))/(1+c_nc_(n-1)))+tan^-1(1/c_n)=tan^-1(x/y)`

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PATHFINDER-TRIGONOMETRIC EQUATION AND INVERSE-QUESTION BANK
  1. Solve: 2cos^2x+5cosx+2 ge 0

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  2. Find the points of intersection of the curves y=cosx and y=sin3x if -p...

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  3. Solve for x and y : 2^(1/cos^2x)sqrt(y^2-y+1//2) le 1

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  4. Find the value of tan^-1(1/2tan2A)+tan^-1(cotA)+tan^-1(cot^3A), for 0 ...

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  5. Solve: sin^-1x+sin^-1(1-x)=cos^-1x

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  6. Prove that: tan^-1((c1x-y)/(c1y+x))+tan^-1((c2-c1)/(1+c2c1))+tan^-1((c...

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  7. The value of 'a' for which ax^2 + sin^-1 (x^2 - 2x + 2) + cos^-1 (x^2 ...

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  8. The number of distinct solutions of the equation 5/4cos^2 2x+cos^4x+si...

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  9. If alpha=3sin^-1(6/(11)) and beta=3cos^-1(4/9), where the inverse trig...

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  10. Let, tan^-1y=tan^-1x+tan^-1((2x)/(1-x^2)), where absx lt 1/sqrt3. Then...

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  11. The number of real solutions of the equation (sinx-x)(cosx-x^2)=0 is

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  12. The values of 2cot^-1 (1/2)-cot^-1 (4/3) is

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  13. The number of distinct roots of abs((sinx, cosx, cosx),(cosx, sinx, co...

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  14. The trigonometric equation sin^-1x=2sin^-1 2a has a real solution if

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  15. Let alpha, beta be two distinct roots of acostheta+bsintheta=c, where ...

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  16. If sin^-1(x/(13))+cosec^-1((13)/(12))=pi/2, then the value of x is

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  17. The value of cot(sum(n=1)^(23)cot^-1(1+sum(k=1)^n2k)) is

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  18. If sin^-1x+sin^-1y+sin^-1z=(3pi)/2, then the value of x^9+y^9+z^9-1/(x...

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  19. Number of solutions of the equation tanx+secx=2cosx, x in [0, pi] is

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  20. The solutions set of inequation cos^-1x lt sin^-1x is

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