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Prove that: cos^(-1)(12/13)+sin^(-1)(3/5...

Prove that: `cos^(-1)(12/13)+sin^(-1)(3/5)=sin^(-1)(56/65)`

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Prove that: cos^(-1)(4/5)+cos^(-1)(12/13)=cos^(-1)(33/65)

Prove that: sin^(-1)(3/5)+sin^(-1)(8/17)=tan^(-1)(77/36) .

2sin^(-1)(4/5)+sin^(-1)(24/25) = __.

Show that "sin"^(-1)(8/17)+"sin"^(-1)(3/5)="cos"^(-1)(36/85) .

Prove that sin^(-1)((4)/(5)) +sin^(-1)((5)/(13)) +sin^(-1)((16)/(65)) =(pi)/(2)

Prove that sin^-1(4/5)+ sin^-1(5/13)+ sin^-1(16/65)= pi/2

Prove the Statement: "sin"^(-1)12/13-"sin"^(-1) 3/5 ="sin"^(-1) 33/65

Prove that ( cos^(-1) ""(3)/(5) + sin^(-1)""(5)/(13) ) = sin^(-1)((63)/(65))

Prove that sin( cos^(-1) ""(3)/(5) + sin^(-1)""(5)/(13) ) = (63)/(65)

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Minimize:Z=6x1+7x2 "Subject to":x1+2x2 ge 4 x1,x2 ge 0

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

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  3. Prove that: cos^(-1)(12/13)+sin^(-1)(3/5)=sin^(-1)(56/65)

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

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  5. Let f be a real function. Prove that f(x)-f(-x) is an odd function and...

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

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  7. Express as a sum of a symmetric and a skew symmetric matrix: [[4,-3],[...

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

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  9. Evaluate abs[[1,a,bc],[1,b,ca],[1,c,ab]]-abs[[1,a,b^2],[1,b,b^2],[1,c,...

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  10. Find the inverse of the matrix [[1,2],[3,4]]

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  11. Find the number of critical points of f(x)=frac[abs(x-1)][x^2]

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  12. If f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):} is continuous...

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  13. Find the equation of the tangent to the curve x = y^2-1 at the point w...

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  14. If y=sin^(-1)(x^3), then find that dy/dx

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  15. If y=e^(x^(e^(x^(e^x)))), then find dy/dx.

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  16. Evaluate int0^2abs(x^2+2x-3)dx

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  17. Find the area of the region bounded by the curve y=sin^(3)x and the st...

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  18. intdx/(1+tanx)

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  19. Evaluate inte^(tan-1)x((1+x+x^2)/(1+x^2))dx.

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

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