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Prove the following statements "cot"^(...

Prove the following statements
`"cot"^(-1)9+"cosec"^(-1)sqrt(41)/(4)=pi/(4)`

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Directions Prove the following "tan"^(-1)1/(4)+"tan"^(-1)2/(9)=1/(2)"cos"^(-1)3/(5)=1/(2)"sin"^(-1)4/(5) .

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Write the value x for which d/dxsin(sin^-1x)=1

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  2. What is the value of int(-1)^(1)ln(frac[4-x][4+x])dx?

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  3. Prove the following statements "cot"^(-1)9+"cosec"^(-1)sqrt(41)/(4)=...

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  4. Show that if R is an equivalence relation on X then dom R=rngR =X.

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  5. Solve graphically: Maximize Z=5x+6y subject to 2x+3yle6,x, yge0

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  6. Solve sin^(-1)(1-x)-2sin^(-1)x=frac[pi][2]

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  7. Let f = {(1,3), (2,4), (3,7)} and g = {(3,2), (4,3), (7,1)} determine ...

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  8. Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c]...

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  9. If abs((a,b,a-b),(b,c,b-c),(2,1,0))=0 , then prove that a,b,c are in G...

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

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  11. Solve : [[7,6,x],[2,x,2],[x,3,7]] = 0

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

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  13. Prove the inequality x^2e^(-x^2) le e^(-1),x in R.

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  14. Prove that d/dxlntan(pi/4+x/2)=secx.

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  15. Determine the point on the curve y = ln x, at which the tangent will b...

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  16. Find the angle of intersection of two curves y =2^x and y=5^x

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  17. If 2y=x(1+(dy)/(dx)), then show that y(2) is a constant.

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  18. Find the solution of the following differential equations: (4x+6y+5)dx...

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

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  20. Solve dy/dx-y=e^x.

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