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Prove that cos^(-1)(frac[b+acosx][a+bcos...

Prove that `cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a+b])tanfrac[x][2])`

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USHA PUBLICATION-PRACTICE PAPER-PRACTICE PAPER
  1. Show that the function f:RRrightarrowRR defined by f(x)={(x^2-frac[1][...

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  2. Solve for x, cos^(-1)x +sin^(-1)((x)/(2)) =(pi)/(6).

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  3. Prove that cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a...

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  4. A diet for a sick person must contain at least 4000 units of vitamins,...

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  5. 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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  6. Find inverse of the following matrices by elementary row/column operat...

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  7. If A =[[1,-2,2],[3,1,-1]] B[[2,4],[1,2],[3,-1]] "verify" "that" (AB)^...

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  8. Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(...

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

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  10. Test differentiability and continuity of the following functions. |1...

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  11. If x =sin t,y = sin 2t then prove that (1-x^2)(d^2y)/(dx^2)- x dy/dx +...

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  12. Find dy/dx if y = x cot^(-1) (x/y)

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  13. Find the point (S) on the curve x=(3at)/(1+t^2), y=(3at^2)/(1+t^2) whe...

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  14. Show that 2sinx+3tanxgt3x for all xin(0,frac[pi][2])

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

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  16. int(pi/5)^(3pi/10) (sinxdx)/(sinx+cosx)

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  17. Find the area of the region bounded by y=6x-x^2x-axis and between ordi...

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  18. Solve : (dy)/(dx)= sin(x+y)+cos(x+y)

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  19. From a differential equation from the equation y=ae^(2x)+be^(-x) by el...

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  20. Prove the following by vector method. An angle inscribed in a semi-cir...

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