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Prove that sec^2(tan^(-1)2)+cos e c^2(co...

Prove that `sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15`

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

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Prove that: tan^(-1) \ 2/3=1/2tan^(-1) \ 12/5

Prove the following : 2cot^(-1)(2)+cosec^(-1)(5/3)=pi/2

Prove that: tan^-1(1/4)+tan^-1(2/9)=1/2 cos^-1(3/5) .

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ALLEN -INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Evaluate the following: cos^(-1)(cos10) (ii) tan^(-1){tan(-6)}

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  2. Evaluate the following: cos^(-1)(cos4)

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  3. Prove that sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15

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

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

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  6. Prove that tan ^(-1) . 1/5 + tan^(-1) . 1/7 + tan ^(-1) . 1/8 = pi/4

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

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

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  9. If x=tan^(- 1)(1)+cos^(- 1)(-1/2)+sin^(- 1)(-1/2) and y=cos[1/2cos...

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

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

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

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

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

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

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

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

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  18. Solve the equation x^(2)+(x/(x-1))^(2)=8

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

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

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