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If (sin^(-1)x)^2+(cos^(-1)x)^2=(17pi^2)/...

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

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`(sin ^{-1} x)^{2}+(cos ^{-1} x)^{2}=frac{17 pi^{2}}{36}`

`implies(sin ^{-1} x)^{2}+(frac{pi}{2}-sin ^{-1} x)^{2}=frac{17 pi^{2}}{36}`

Let `sin ^{-1} x=y`
`therefore(y)^{2}+(frac{pi}{2}-y)^{2}=frac{17 pi^{2}}{36}`

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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. 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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  2. If cot(cos^(-1)(3/5)+sin^(-1)x)=0 , find the values of xdot

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Prove that : tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4dot

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  16. tan^-1 (3/4) + tan^-1 (3/5) + tan^-1 (8/19)

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

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  18. Prove that : cot^(-1)7+cot^(-1)8+cot^(-1)18=cot^(-1)3

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  19. Prove that: tan^(-1)(1-x)/(1+x)-tan^(-1)(1-y)/(1+y)=sin^(-1)(y-x)/(sqr...

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  20. If a > b > c >0 , prove that cot^(-1)((a b+1)/(a-b))+cot^(-1)((b c+1)...

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