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Prove that tanAcdottan(A+60^@)+tanAcdott...

Prove that `tanAcdottan(A+60^@)+tanAcdottan(A-60^@)+tan(A+60^@)tan(A-60^@)=-3`

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PATHFINDER-BASIC MATHEMATICS-QUESTION BANK
  1. Prove that tan 1^@ tan 2^@ tan 3^@........ tan 88^@tan89^@=1

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  2. Prove that sin10^@+sin20^@+sin30^@+.........+sin360^@=0

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  3. Prove that tanAcdottan(A+60^@)+tanAcdottan(A-60^@)+tan(A+60^@)tan(A-60...

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  4. If the angle theta be divided into two parts such that the tangent of ...

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  5. If cos theta+ cos^2 theta=1, prove that sin^12 theta+3sin^10 theta+3s...

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  6. Evaluate : lim(x rarr 0)(3sin^-1 x)/(4(e^x-1))

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  7. Evaluate : lim(x rarr 0)log(1+5 x)/(e^(2x)-1)

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  8. Evaluate : lim(xrarr0) (sin(1+x)-sin(1-x))/x

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  9. Evaluate : lim(xrarr0) (tanx-sinx)/x^3

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  10. Differentiate the following functions w.r.t.'x' : cossqrt((x^2+3x+4)...

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  11. Differentiate the following functions w.r.t.'x' : (xsin^-1x)/(sqrt(1...

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  12. Differentiate the following functions w.r.t.'x' : log (sin (logx))

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  13. Differentiate the following functions w.r.t.'x' : e^(3sqrtax)

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  14. Find dy/dx: y=(tanx)^(cotx)+(cotx)^(tanx)

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  15. Find dy/dx: y=(logx)^x

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  16. Find dy/dx: x^3+y^3=3axy

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  17. If sin y = x sin(a+y), than prove that dy/dx=(sin^2(a+y))/sina

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  18. Find the derivative of tan^-1((2x)/(1-x^2)) w.r.t. sin^-1((2x)/(1+x^2)...

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  19. Show that x/(1+x)ltlog(1+x)ltxforallxgt0.

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  20. Find the equations of tangent and normal to the curve y(x-2)(x-3)-x+7=...

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