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Evaluate: tan^(-1)((3sin2alpha)/(5+3cos2...

Evaluate: `tan^(-1)((3sin2alpha)/(5+3cos2alpha))+tan^(-1)(1/4 tan alpha),`

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To evaluate the expression \[ \tan^{-1}\left(\frac{3\sin(2\alpha)}{5 + 3\cos(2\alpha)}\right) + \tan^{-1}\left(\frac{1}{4}\tan(\alpha)\right), \] we will follow these steps: ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+...

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  2. If cj >0 for i=1,2,....., n prove that tan^(-1)((c1x-y)/(c1y+x)...

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  3. Evaluate: tan^(-1)((3sin2alpha)/(5+3cos2alpha))+tan^(-1)(1/4 tan alpha...

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  4. Prove that: sum(m=1)^ntan^(-1)((2m)/(m^4+m^2+2))=tan^(-1)((n^2+n)/(n^2...

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  5. Sum the following series to infinity: tan^(-1)1/(1+1+1^2)+tan^(-1)1/(...

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  6. Solve the equation: tan^(-1)sqrt(x^2+x)+sin^(-1)sqrt(x^2+x+1)=pi/2

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  7. If a1,a2,a3, an are in arithmetic progression with common difference d...

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  8. Prove that: tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x...

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  9. If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)...

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  10. Find the maximum and minimum values of (sin^(-1)x)^3+(cos^(-1)x)^3, wh...

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  11. the greatest and least values of (sin^(-1) x)^2+(cos^(-1)x)^2

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  12. Solve : 4sin^(-1)x=pi-cos^(-1)x

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  13. If (sin^(-1)x)^2+(cos^(-1)x)^2=(17pi^2)/(36) , find xdot

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  14. Prove that : tan^(-1)2+tan^(-1)3=(3pi)/4

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  15. Prove that : tan^(-1)(2/11)+tan^(-1)(7/24)=tan^(-1)(1/2)

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  16. Prove that: sin^(-1)(12)/(13)+cos^(-1)4/5+tan^(-1)(63)/(16)=pi

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  17. Prove that: tan^(-1)1+tan^(-1)2+tan^(-1)3=pi

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  18. Prove that: tan^(-1)1/7+tan^(-1)1/(13)=tan^(-1)2/9 tan^(-1)+tan^(-1...

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  19. If tan^(-1)2+tan^(-1)3+theta=pi, find the value of thetadot

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  20. What is greater, tan1 or tan^(-1)1?

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