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Prove that : sin^(-1) ""(x)/(sqrt(1 + x^...

Prove that : `sin^(-1) ""(x)/(sqrt(1 + x^(2))) + cos ^(-1) "" (x + 1)/( sqrt( x^(2) + 2x + 2)) = tan^(-1) ( x^(2) + x + 1)`

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ICSE-MODEL TEST PAPER - 8-Section - A
  1. Using differential find the approximate value of tan 46^(@) , If it ...

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  2. A ladder 13 m long is leaning against a wall. The bottom of the ladder...

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  3. A function f :R to R is defined by f(x) = 2x^(3) + 3 . Show that f i...

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  4. If y = cos^(-1) ((1)/( sqrt(1+t^(2)))), x = sin^(-1) (sqrt((t^(2))/(1 ...

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  5. Evaluate : int(0)^((pi)/2)) (sqrt(cot x))/(sqrt(cot x)+ sqrt(tan x)) ...

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  6. Evaluate intsec ^(2) x * cosec^(2) x dx

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  7. Solve the differential equation : (1 - x^(2)) (dy)/(dx) - xy = x

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  8. Prove that : sin^(-1) ""(x)/(sqrt(1 + x^(2))) + cos ^(-1) "" (x + 1)/(...

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  9. Evaluate : int (-2)^(3) |1 - x^(2) | dx

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  10. If y = e^(x) (sin x + cos x ), prove that (d^(2) y)/( dx^(2)) - 2 (...

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  11. Is the function f (x) = ( 3 x + 4 tan x)/( x) continuous at x = 0 ? ...

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  12. A die is thrown twice and the sum of number appearing is observed to b...

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  13. A coin is tossed until a head appears or tail appears 4 times in succe...

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  14. Show that x = 2 is a root of the equation|{:(x, -6, -1),(2,- 3x,x-3),(...

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  15. Solve the following system of equations by matrix inversion method. ...

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  16. Evaluate : int (sqrt(1 + sin x))/( 1 + cos x) e^(-(x)/(2))dx

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  17. Evaluate : int ( sqrt( tan x) - sqrt( cot x)) dx

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  18. A window is in the form of a rectangle, together with a semi-circle on...

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  19. Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin ...

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