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Prove that tan^-1 ((3sin2x)/(5+3 cos2x))...

Prove that `tan^-1 ((3sin2x)/(5+3 cos2x)) + tan^-1(1/4 tanx = x`.

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UNITED BOOK HOUSE-MISCELLANEOUS EXERCISE-EXERCISE
  1. Find the number of quivalance relations on the set A = {a,b,c} contain...

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  2. If f(x) = sin x, g(x) = x^2 and h(x), = logx, find the composite funct...

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  3. Prove that tan^-1 ((3sin2x)/(5+3 cos2x)) + tan^-1(1/4 tanx = x.

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  4. If cos^-1 x +cos^-1y + cos^-1z = pi and x + y + z = 3/2, then show tha...

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  5. Solve : cos^-1 x - sin^-1 x = cos^-1 (x sqrt3).

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  6. If phi = tan^-1 (xsqrt3)/(2k-x) and theta (2x-k)/(ksqrt3), then show t...

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  7. By using properties of determinats. Prove that- |(x+4,2x,2x),(2x,x+4...

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  8. By using properties of determinats. Prove that- |(1,1+x,1+x+y),(2,3+...

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  9. By using properties of determinats. Prove that- |(sintheta,costheta,...

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  10. Let X = [(3,2,5),(4,1,3),(0,6,-7):}] express X as sum of two matrics s...

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  11. If [(2,-1),(1,0),(-3,4):}]xxP= [(-1,-8,-10),(1,-2,-5),(9,22,15):}], fi...

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  12. Prove that: underset(xrarrinfty)lim sqrtx (sqrt(x+3) - sqrtx)= 3/2

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  13. Prove that:underset(x rarr0)lim ((x-1+cosx)/(x))^(1/x) = e^(-1/2)

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  14. Prove that: underset(xrarrinfty)lim ((x+5)/(x+1))^x = e^4

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  15. Prove that: underset(xrarrpi/2)lim (1+cosx)^(3secx) = e^3

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  16. Prove that: underset(xrarr0)lim ([1+3x]^((x+3)/x))= e^9

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  17. Evaluate the following limits: underset(x rarr0)lim(xe^x - log(x+1))/(...

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  18. Evaluate the following limits: underset(x rarr0)lim[tan(pi/4+x)]^(1/x)

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  19. Evaluate the following limits: underset(x rarr0)lim(sinx + cos x)^(1/x...

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  20. Evaluate the following limits: underset(x rarr0)limsinlog(1+x)/log(sin...

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