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Prove the following: (9pi)/8-9/4sin^(-1...

Prove the following: `(9pi)/8-9/4sin^(-1)(1/3)=9/4sin^(-1)((2\ sqrt(2))/3)`

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Prove that: (9pi)/8-9/4sin^(-1)(1/3)=9/4sin^(-1)((2sqrt(2))/3)

Prove that: (9pi)/8-9/4sin^(-1)1/3=9/4sin^(-1)(2sqrt(2))/3

Prove the following: tan^(-1)(1/4)+tan^(-1)(2/9)=1/2cos^(-1)(3/5)

Prove the following : sin^(-1)(4/5)+2\ tan^(-1)(1/3)=pi/2

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

sin^(-1)(sin((9pi)/4))

Prove: tan^(-1)(1/4)+tan^(-1)(2/9)=sin^(-1)(1/sqrt(5))

Solve the following equations: sin^(-1)((3x)/5)+sin^(-1)((4x)/5)=sin^(-1)x sin^(-1)6x+sin^(-1)6sqrt(3)x=pi/2

Find the principal value of each of the following: sin^(-1)((sqrt(3)+1)/(2sqrt(2))) (ii) sin^(-1)(cos(pi/4)) (iii) sin^(-1)(tan((5pi)/4))

Prove that tan^(-1) (1/4) + tan^(-1) (2/9) = 1/2 sin^(-1) (4/5)

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Let f: R rarr R be defined as f(x)=10 x+7. Find the function g: R ra...

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  2. Solve the equation tan^(-1)((1-x)/(1+x))=1/2tan^(-1)x ,(x >0)

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  3. Prove the following: (9pi)/8-9/4sin^(-1)(1/3)=9/4sin^(-1)((2\ sqrt(2)...

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  4. Evaluate: int(x^2)/((x^2+4)\ (x^2+9))dx

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  5. If tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=pi/4, then find the val...

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  6. If y=cot^(-1)(sqrt(cos"x"))-tan^(-1)(sqrt(cos"x")), prove that siny=ta...

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  7. Find the image of the point having position vector hat i+2 hat j+4 ha...

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  8. Find the equation of a plane which is at a distance of 3\ sqrt(3) unit...

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  9. Evaluate : int xsin^(-1)\ x\ \ dx

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  10. Evaluate : int(dx)/(sqrt(5-4x-2x^2))

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  11. Prove that the radius of the right circular cylinder of greatest cu...

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  12. The amount of pollution content added in air in a city due to x diesel...

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  13. An open box with a square base is to be made out of a given quantity...

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  14. Solve the following differential equation: (dy)/(dx)+ycotx=4x\ cos e c...

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  15. Find the particular solution of the differential equation: (1+e^(2x))d...

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  16. Let vec a= hat i+4 hat j+2 hat k ,\ \ vec b=3 hat i-\ 2 hat j+7 hat ...

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  17. If vec a= hat i+ hat j+ hat k ,\ \ vec b=4 hat i-\ 2 hat j+3 hat k a...

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  18. Prove, using properties of determinants: |[y+k, y, y],[ y, y+k, y],[...

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  19. Consider f: R^+ rarr [4, oo] given by f(x)=x^2+4. Show that f is inver...

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  20. What are the direction cosines of a line, which makes equal angles ...

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