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Express the following functions in the s...

Express the following functions in the simplest form :
`tan^-1 (a cosx - b sin x)/(b cos x + a sin x ), - pi/2 < x < pi/2` and `a/b tan x > -1`

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PRADEEP PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. Express the following functions in the simplest form : tan^-1(3x - x...

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  2. Express the following functions in the simplest form : tan^-1 ((3a^2...

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  3. Express the following functions in the simplest form : tan^-1 (a cos...

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  4. Solve : cot^-1(2x)+cot^-1(3x)=pi/4

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  5. Solve the following equations. cot^-1 x - cot^-1 (x+2) = pi/12, x > ...

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  6. Solve the following equations: tan^-1((1-x)/(1+x)) = 1/2 tan^-1 x, x...

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  7. Solve the 2 tan^-1 (cos x) = tan^-1 (2 cosec x).

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  8. Solve the following equations. cos^-1((1-x^2)/(1+x^2)) + tan^-1 ((2x...

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  9. Solve : 3 tan^-1(1/(2+sqrt3)) - tan^-1(1/x) = tan^-1(1/3)

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  10. Solve the following equations. tan^-1 (x-1) + tan^-1 x + tan^-1 (x+1...

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  11. Solve the following equations. tan^-1 (sqrt(x^2 + x) + sin^-1 sqrt(x...

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  12. Solve the following equations. tan^-1 (x-1)/(x-2) + tan6-1 (x+1)/(x+...

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  13. Solve : ((tan^-1 ((2x-3)/(2x-5)) + tan^-1((2x+3)/(2x+5)))=pi/4) .

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  14. Solve the following equations. cos(tan^-1x) = sin (cot^-1 (3//4)

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  15. Solve the following equations: tan^-1(x+1) + tan^-1 (x-1) = tan^-1 (...

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  16. Prove that for 0 < a < b < c cot^-1 (1+ab)/(a-b) + cot^-1 (1+bc)/(b-...

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  17. If tan^-1x + tan^-1y + tan^-1z = pi, then prove that: x + y + z = xyz.

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  18. Find the value of the following: tan1/2[sin^-1(2x/(1+x^2)) + cos^-1(1-...

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  19. Prove that : tan^-1[(sqrt(1+x^2) - sqrt(1-x^2))/(sqrt1+x^2 + sqrt(1-x^...

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  20. Prove the following: cos[tan^-1{sin(cot^-1x)}]=sqrt((1+x^2)/(2+x^2))

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