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Prove that : "cos"^(-1) ((b+a "cos"x)/(...

Prove that :
`"cos"^(-1) ((b+a "cos"x)/(a+b "cos"x))`
` =2"tan"^(-1)(sqrt((a-b)/(a+b)) "tan" x/2)

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Verified by Experts

The correct Answer is:
`= cos^(-1) ((a cos x + b)/(a + b cos x)) = LHS`
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ARIHANT PUBLICATION-CHSE ODISHA EXAMINATION PAPER 2019-Group B (60 Marks)
  1. Prove that : "cos"^(-1) ((b+a "cos"x)/(a+b "cos"x)) =2"tan"^(-1)(sqr...

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  2. Two types of food X and Y are mixed to prepare a mixture in such a wa...

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  3. Construct the multiplication table X7 on the set {1, 2, 3, 4, 5, 6}. A...

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  4. Let R be the relation on the set R of real numbers such that aRb iff a...

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  5. Solve for x, 2 tan ^(-1)(cos x) =tan^(-1) (2"cosec"x).

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  6. Find the probability distribution of number of heads in three tosses...

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  7. If A=[{:(1,2,0),(0,1,3),(-2,5,3):}] then verify that A+A is symmetric ...

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  8. If A=[{:(1,2,3),(3,-2,1),(4,2,1):}] then show that A^(3)-23A-40I=O

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  9. Solve the following : [[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^...

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  10. A person takes 4 tests in succession. The probability of his passing t...

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  11. Find the point on the curve x^2 + y^2 - 4xy + 2 = 0 where the normal...

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  12. Find the intervals in which the function y=(lnx)/(x) is increasing and...

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

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  14. Find (d^2y)/(dx^2) if x=a costheta,y=bsintheta.

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  15. Verify lagrange's Mean-Value theorem for F(x) = x^3 - 2x^2 - x + 3 o...

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  16. Find differential equation of the curve y=ae^(3x)+be^(5x).

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  17. Solve : (y^(2) + 7 y + 12) dy + x dx = 0

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  18. Evaluate : int ((2 x + 1) dx)/( ( sqrt( x^(2) + x + 4)))

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  19. Evaluate : int(0)^(pi) ( cos x dx)/(( 2 - sin x) (3 + sin x))

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  20. Find the area of the region bounded by the curve y=6x-x^2 and the x-ax...

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