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If cos^-1x+cos^-1y+cos^-1z=pi, prove tha...

If `cos^-1x+cos^-1y+cos^-1z=pi`, prove that `x^2+y^2+z^2+2xyz=1`.

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. What is the interval in which y=sinx,x"in[0,2pi]is increasing?

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  2. What is the value of int-1^1xabsxdx

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  3. If cos^-1x+cos^-1y+cos^-1z=pi, prove that x^2+y^2+z^2+2xyz=1.

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  4. Find the domain of the functionf(x)=sqrt(log(12/(x^2-x))).

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  5. Solve the pair of these equationsx+y=10,3x+y=12,

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  6. Show that sin^(-1)(1/sqrt(10))+cos^(-1)(2/sqrt5)=pi/4.

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  7. If a relation R:AtoAis an equivalence relation then prove that R^-1:A ...

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  8. Verify that [AB]^T = B^T A^T whereA=[[1,2,3],[3,-2,1]],B=[[1,2],[2,0],...

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  9. Verify that [AB]^T = B^T A^T whereA=[[1,2,3],[3,-2,1]],B=[[1,2],[2,0],...

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  10. alpha = 0.9. The value of beta is

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  11. If Aand B are both symmetric matrices of same oder,then prove that AB...

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  12. If ABC is a triangle, then prove that abs[[tanA,1,1],[1,tanB,1],[1,1,...

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  13. Solve by matrix method 2x+y=5,x-y=1

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  14. Find the point on the curve y^2 - x^2 + 2x - 1 =0 where the tangent ...

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  16. If y=tan^(-1)(cosx/(1+sinx)),then prove that dy/dx=-1/2

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  17. Examine the continuity of the following functions at indicated points....

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  18. If f(x+y)=f(x)f(y)for all real x,y,f(2)=3,f'(0)=1 then what is the val...

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  19. Find the area of the circle x^2+y^2=2ax.

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  20. intdx/(sqrtx-root(3)(x))(x=t^6)

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