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If x=cos e c[tan^(-1){"cos"(cot^(-1)(sec...

If `x=cos e c[tan^(-1){"cos"(cot^(-1)(sec(sin^(-1)a)))}]` and `y="sec"[cot^(-1){"sin"(tan^(-1)(cos e c(cos^(-1)a)))}]` then find the relation between x and y

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ALLEN-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Prove that: sin^(-1)(12)/(13)+cos^(-1)4/5+tan^(-1)(63)/(16)=pi

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

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

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  4. Evaluate: (i)tan{2tan^(-1)(1/5)-pi/4} (ii) tan{1/2cos^(-1)(sqrt(5)/3)...

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  5. Evaluate: {(2tan^(-1)1)/5-pi/4} (ii) tan{1/2cos^(-1)(sqrt(5))/3}

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

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

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

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  9. Prove the following: 2\ tan^(-1)1/5+sec^(-1)(5sqrt(2))/7+2\ tan^(-1)1/...

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

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

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

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

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

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

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

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

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

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

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

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