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Prove that cos tan^(-1)sin cot^(-1)x=sqr...

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

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SHARAM PUBLICATION-MODEL QUESTION PAPER 12-EXERCISE
  1. Let f(x) =sqrtx ,g(x)=1-x^2. Compute fog and gof .

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  2. Consider the binary operation ** on the set {1, 2, 3, 4 5} defined by ...

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  3. Prove that cos tan^(-1)sin cot^(-1)x=sqrt((1+x^2)/(2+x^2).

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  4. Solve the LPP Maximize z=3x+2y Subject to x+yle400 2x+yle500 ,xge0...

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  5. If the matrix A is such that [[1,-1],[2,3]]A=[[-4,1],[7,7]], find A.

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  6. Verify that A=[[a,b],[c,d]] satisfies the equation A^2-(a+d)A+(ad-bc...

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  7. Factorise the determinant |[x^3-a^3,x^2,x],[b^2-a^3,b^2,b],[c^3-a^3,c^...

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  8. Factorize the following. [[x+a,b,c],[b,x+c,a],[c,a,x+b]]

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  9. If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O

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  10. Find the value of k if the function f(x) defined by f(x)={(2x-1,whenx<...

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  11. If sin y = x sin (a + y) then show that (dy)/(dx)=(sin^2(a+y))/(sina)

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  12. If y^2cot x = x^2 coty then find (dy)/(dx)

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  13. Find the intervals where function is increasing function y = cos x + s...

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  14. Find the equation of the normal to the curve 5x^2+3y^2=23 at (2,-1)

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  15. Integrate int sec xtanx.sqrt(tan^2x-3).dx

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  16. int(xe^x)/(1+x^2)dx

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  17. Evaluate int0^1[tan^-1x+x/(1+x^2)]dx

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  18. Find the area of region enclosed by y^2 = 4ax and x^2 = 4ay.

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  19. Find the particular solution of the following differential equation : ...

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  20. If the sum of two unit vectors is a unit vectors find the magnitude of...

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