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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: {(2tan^(-1)1)/5-pi/4} (ii) tan{1/2cos^(-1)(sqrt(5))/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 the following: 2\ tan^(-1)1/5+sec^(-1)(5sqrt(2))/7+2\ tan^(-1)1/...

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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 : 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. solve sin^(-1) (sin 5) gt x^(2) - 4x

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  10. The complete solution set of the inequality [cot^(-)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 ci >0 for i=1,2,....., n prove that tan^(-1)((c1x-y)/(c1y+x))+tan^...

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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. The greater of the two angles A=2tan^(-1)(2sqrt(2)-1) and B=3sin^(-1)(...

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  15. Solve for x : If [ sin^(-1) cos^(-1) sin ^(-1) tan^(-1)x] = 1, where...

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

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  17. The principle value of sin^-1 (sqrt-(3)/2) is (A) - (2pi)/3 (B) pi/3 ...

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  18. Show that : cos(2\ tan^(-1)(1/7 ))=sin(4\ tan^(-1) (1/3) )

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  19. The value 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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