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Evaluate: (i) cot(sin^(-1)(3/4)+sec^(-1)...

Evaluate: (i) `cot(sin^(-1)(3/4)+sec^(-1)(4/3))` (ii) `sin(tan^(-1)x+tan^(-1)(1/x))` for `x<0`

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(i) Given as
`cot (sin ^{-1}(3 / 4)+sec ^{-1}(4 / 3))`
`implies cot (sin ^{-1} frac{3}{4}+cos ^{-1} frac{3}{4})`

`(because sec ^{-1} x=cos ^{-1} frac{1}{x})`

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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. the greatest and least values of (sin^(-1) x)^2+(cos^(-1)x)^2

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  2. Find the maximum and minimum values of (sin^(-1)x)^3+(cos^(-1)x)^3, wh...

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  3. Evaluate: (i) cot(sin^(-1)(3/4)+sec^(-1)(4/3)) (ii) sin(tan^(-1)x+tan...

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  4. Evaluate: (i) sin(tan^(-1)x+tan^(-1)(1/x)) for x >0 (ii) cot(tan^(-1...

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  5. Evaluate: cos(sec^(-1)x+"c o s e c"^(-1)x) , |x|geq1

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  6. If -1lt=x , ylt=1 such that sin^(-1)x+sin^(-1)y=pi/2, find the value o...

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  7. If sin^(-1)x+sin^(-1)y=pi/3 and cos^(-1)x-cos^(-1)y=pi/6 , find the va...

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  8. If cot(cos^(-1)(3/5)+sin^(-1)x)=0 , find the values of xdot

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  9. If (sin^(-1)x)^2+(cos^(-1)x)^2=(17pi^2)/(36) , find xdot

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  10. If sin(sin^(-1)(1/5)+cos^(-1)(x))=1 Find the value of x.

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  11. Solve: sin^(-1)x=pi/6+cos^(-1)x

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  12. Solve : 4sin^(-1)x=pi-cos^(-1)x

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  13. Solve: tan^(-1)x+2cot^(-1)x=(2pi)/3

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  14. Solve: 5tan^(-1)x+3cot^(-1)x=2pi

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  15. Prove that: tan^(-1)(2/(11))+tan^(-1)(7/(24))=tan^(-1)(1/2)

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  16. Prove that : tan^(-1)2+tan^(-1)3=(3pi)/4

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  17. Prove that : tan^(-1)1+tan^(-1)2+tan^(-1)3=pi

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

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  19. If tan^(-1)2+tan^(-1)3+theta=pi find the value of thetadot

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

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