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Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-...

Prove that `tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2) cos^(-1)((a)/(b))}=(2b)/(a)`.

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ARIHANT PUBLICATION-SAMPLE PAPER 3 -SHORT ANSWER TYPE QUESTIONS
  1. Answer any one question : Evaluate int(0)^(3) (2x^(3) + 3x +5) dx .

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  2. Let f : R to R be a function given by f (x) = ax + b for all x in R. F...

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  3. Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2...

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  4. Answer the question : Evaluate int(2x^(3) + 3x^(2) +5) dx

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  6. Show that |{:(1,x, x ^(3)),(1,y,y ^(3)),(1,z,z^(3)):}| = (x-y) (y-z) (...

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  11. Show that the function f(x) given by f(x)={:{(x" sin "(1)/(x)", if ...

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  12. Show that the line (x)/(a) + (y)/(b) = 1, touches the curve y = be^(-x...

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  13. If f(x) = a In x + bx^2 + x has extreme values at x= - 1 and x = 2 the...

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  14. If x = 3 sin t - sin 3t, y = 3 cos t - cos 3t, find (dy)/(dx) at t = (...

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  15. Evaluate int(2x^(3) + 3x^(2) +5x+2) dx

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  16. Solve the following differerntial equation x (dy)/(dx) + y = x cos x +...

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  17. Evaluate int (x ^(2) +1)/( (x +1) ^(2)) dx

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  18. Evaluateint (cosxtan x )/((sec x + tan x )) dx

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  19. Find the area of region included between the parabola 4y = 3x^(2) and ...

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  20. Find the direction consines of the perpendicular from the origin to th...

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