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Prove that: tan^(-1)sqrt(x)=1/2cos^(-1)(...

Prove that: `tan^(-1)sqrt(x)=1/2cos^(-1)((1-x)/(1+x)), x in [0,1]`

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ALLEN-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Evaluate: tan{1/2cos^(-1)(sqrt5/3)}

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  2. Prove that: 2tan^(-1)1/2+tan^(-1)1/7=tan^(-1)(31)/(17)

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  3. Prove that: tan^(-1)sqrt(x)=1/2cos^(-1)((1-x)/(1+x)), x in [0,1]

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  4. Find the value of 4tan^(-1)1/5-tan^(-1)1/(70)+tan^(-1)1/(99)

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  5. Prove that :2tan^(-1)(1/5)+sec^(-1)((5sqrt(2))/7)+2tan^(-1)\ 1/8=pi/4

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  6. The equation 2cos^(-1)x+sin^(-1)x=(11pi)/6 has a. no solution b. only...

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

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  8. Solve the equation : 2 tan^(-1) ( 2x - 1) = cos ^(-1) x .

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  9. Find the complete solution set of sin^(-1)(sin5)> x^2-4x

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  10. The complete solution set of the inequality [cot^(-1)x]^2-6[cot^(-1)x]...

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  11. If cot^(-1)n/pi>pi/6,n in N , then the maximum value of n is 6 (b) ...

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  12. If cj >0 for i=1,2,....., n prove that tan^(-1)((c1x-y)/(c1y+x)...

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  13. If tan^(-1)y=4tan^(-1)x(|x|<tanpi/8) , find y as an algebraic function...

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  14. If A=2tan^(-1)(2sqrt(2)-1)a n dB=3sin^(-1)(1/3)+sin^(-1)(3/5), then wh...

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  15. If [sin^-1 (cos^-1(sin^-1 (tan^-1 x)))]=1, where [*] denotes the gre...

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  16. The value (s) of theta satisfying the equation theta=tan^(- 1)(2tan^2t...

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  17. Transform sin^(-1)x in other inverse trigonometric function, where x i...

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  18. The value of sin^(-1)(-sqrt(3)/2)\ is: (A) (-pi)/3 (B) (-2pi)/3 (...

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  19. The vale of sec(sin^-1(sin((-50pi)/9))+cos^-1(cos(31pi)/9))

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  20. cos (cos^-1 cos((8pi)/7) +tan^-1 tan(8pi/7)) has the value equal to -

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