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Prove that: tan^(-1)x+tan^(-1)1/x={pi/2,...

Prove that: `tan^(-1)x+tan^(-1)1/x={pi/2,ifx >0-pi/2,ifx<0`

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ALLEN-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Prove that sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15

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  2. Find the number of solutions of (x ,\ y) which satisfy |y|=cosx\ a n d...

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  3. Prove that: tan^(-1)x+tan^(-1)1/x={pi/2,ifx >0-pi/2,ifx<0

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  4. Prove that tan^-1(1/7)+tan^-1(1/13)=tan^-1(2/9)

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  5. Prove that: tan^(-1)(1/5)+tan^(-1)(1/7)+tan^(-1)(1/3)+tan^(-1)(1/8)=p...

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  6. Prove that: sin^(-1)(12)/(13)+cos^(-1)4/5+tan^(-1)(63)/(16)=pi

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  7. Prove that: cos^(-1)(12)/(13)+sin^(-1)3/5=sin^(-1)(56)/(65)

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  8. If x=cos e c[tan^(-1){"cos"(cot^(-1)(sec(sin^(-1)a)))}] and y="sec"[...

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  9. Evaluate: tan{2tan^(-1)(1/5)-pi/4}

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  10. Evaluate: tan{1/2cos^(-1)(sqrt5/3)}

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

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

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

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

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

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

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

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

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

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

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