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If sin^(-1)x+sin^(-1)y+sin^(-1)z = pi th...

If `sin^(-1)x+sin^(-1)y+sin^(-1)z = pi` then prove that
`xsqrt(1-x^2)+ysqrt(1-y^2)+zsqrt(1-z^2)= 2xyz`.

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UNITED BOOK HOUSE-QUESTION PAPER 2016-EXERCISE
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  2. A relation R is defined on the set of all natural numbers IN by: (x,y)...

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  3. If sin^(-1)x+sin^(-1)y+sin^(-1)z = pi then prove that xsqrt(1-x^2)+...

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  4. Express the matric A= [[-3,4,1],[2,3,0],[1,4,5]] as the sum of a symme...

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  5. If p,q,r are not in geometric progression and |[1,q/p,alpha+q/p],[1,r/...

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  6. Prove that,abs((a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1))=1+a^2+b^2+c^...

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  7. If siny = x sin(a+y) then show that (dy)/(dx)= (sina)/(1-2xcos a+x^2).

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  8. pv^a=c (a and c are constants) then show that v^2(d^2p)/(dv^2)=a(a+1)...

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  9. Evaluate: inte^x(x-3)/(x-1)^3 dx

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  10. Evaluate: int sqrt(1+cosecx dx)

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  11. Solve: (1+3e^(y//x))dy+3e^(y//x)(1-y/x)dx=0

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  12. If the area of a circle increases uniformly, then show that the rate o...

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  13. The vectors veca,vecb,vecc are such that veca+vecb+vecc=vec0, If |vec...

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  14. If vec alpha = lambda hat i+hatj+3 hatk,vec beta= -hati+2hatj+hatk,vec...

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  15. Evaluate (with the help of definite integral): underset(n rarr infty)l...

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  16. Evaluate: overset(3pi/4)underset(pi/4)int theta/(1+sintheta)d theta

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  17. if a and b are any two constants, then prove that Var (aX+b)=a^2Var(X)...

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  18. Minimize the following objective function Z graphically: (Graph sheet ...

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  19. If the normal at any point to the curve x^(2//3)+y^(2//3)=a^(2//3) mak...

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  20. find the volume of the largest cylinder inscribed in the sphere of rad...

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