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Simplify [(3 sin 2 alpha)/(5 + 3 cos 2...

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`[(3 sin 2 alpha)/(5 + 3 cos 2 alpha)] + tan^(-1) [(tan alpha)/(4)], " where " -(pi)/(2) lt alpha lt (pi)/(2)`

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To simplify the expression \[ \left[\frac{3 \sin 2\alpha}{5 + 3 \cos 2\alpha}\right] + \tan^{-1}\left(\frac{\tan \alpha}{4}\right) \] we will follow these steps: ...
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CENGAGE ENGLISH-INVERSE TRIGONOMETRIC FUNCTIONS-Illustration
  1. Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(cota)+tan^(-1)(cot^3A)={ when ...

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  2. Let a, b and c be positive real numbers. Then prove that tan^(-1) sqrt...

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  3. Simplify [(3 sin 2 alpha)/(5 + 3 cos 2 alpha)] + tan^(-1) [(tan alph...

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  4. Solve the equation tan^(-1) 2x + tan^(-1) 3x = pi//4

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  5. Solve tan^(-1) x + sin^(-1) x = tan^(-1) 2x

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  6. Solve cot^(-1) ((3x^(2) + 1)/(x)) = cot^(-1) ((1 - 3x^(2))/(x)) - tan^...

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  7. If x gt y gt z gt 0, then find the value of "cot"^(-1) (xy + 1)/(x - y...

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  8. Solve tan^(-1) x + cot^(-1) (-|x|) = 2 tan^(-1) 6x

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  9. If a(1), a(2), a(3),...., a(n) is an A.P. with common difference d, th...

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  10. Find the value of sum(r=0)^(oo) tan^(-1) ((1)/(1 + r + r^(2)))

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  11. Find the sum sum(r =1)^(oo) tan^(-1) ((2(2r -1))/(4 + r^(2) (r^(2) -2r...

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  12. Find the value of 4 tan^(-1).(1)/(5) - tan^(-1).(1)/(70) + tan^(-1).(1...

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  13. If (x -1) (x^(2) + 1) gt 0, then find the value of sin((1)/(2) tan^(-1...

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  14. Prove that 3 tan^(-1) x= {(tan^(-1) ((3x - x^(3))/(1 - 3x^(2))),"if ...

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  15. Prove that cot^(-1).(3)/(4) + sin^(-1).(5)/(13) = sin^(-1).(63)/(65)

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  16. Solve : sin^(-1)x + sin^(-1) 2x = (pi)/(3)

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  17. Solve sin^(-1) x + sin^(-1) (1 - x) = cos^(-1) x

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  18. Solve : cos^(-1)(1/2x^2+sqrt(1-x^2).sqrt(1-(x^2)/4))=cos^(-1)x/2-cos^(...

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  19. If x in (0, (pi)/(2)), then show that cos^(-1) ((7)/(2) (1 + cos 2 x) ...

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  20. Which of the following angles is greater ? theta(1) = sin^(-1).(4)/(...

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