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Prove the following: cos[tan^-1{sin(cot^...

Prove the following: `cos[tan^-1{sin(cot^-1x)}]=sqrt((1+x^2)/(2+x^2))`

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ACCURATE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTIONS CARRYING 4 MARKS
  1. If sin[cot^(-1)(x+1)]=cos(tan^(-1)x), then find x.

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  2. Solve the following equation cos(tan^(-1)x)=sin(cot^(-1)""3/4).

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  3. Solve the following equations : (i) 2tan^(-1)(cos(2x))=tan^(-1)(2cos...

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  4. Prove that : sin^(-1)""8/17+sin^(-1)""3/5=sin^(-1)""77/85=tan^(-1)""77...

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  5. Prove that : sin^(-1)""3/5+sin^(-1)""8/17=cos^(-1)""36/85.

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  6. Write the value of tan^(-1)[2sin(2cos^(-1)""sqrt(3)/2)].

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  7. Write the principle value of tan^(-1)(1)+cos^(-1)(-1/2).

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  8. Find the value of the following : tan^(-1)(1)+cos^(-1)(-1/2)+sin^(-1...

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  9. Find the value of the following : cos^(-1)(1/2)+2sin^(-1)(1/2)

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  10. Find the value of the following : cos^(-1)(1/2)-2sin^(-1)(1/2)

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  11. Write the value of cos^(-1)(-1/2)+2sin^(-1)(1/2)

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  12. Prove the following: cos[tan^-1{sin(cot^-1x)}]=sqrt((1+x^2)/(2+x^2))

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  13. If sin[cot^(-1)(x+1)]=cos(tan^(-1)x), then find x.

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  14. Solve the following equation cos(tan^(-1)x)=sin(cot^(-1)""3/4).

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  15. Solve the following equations : (i) 2tan^(-1)(cos(2x))=tan^(-1)(2cos...

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  16. Prove that : sin^(-1)""8/17+sin^(-1)""3/5=sin^(-1)""77/85=tan^(-1)""77...

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  17. Prove that : sin^(-1)""3/5+sin^(-1)""8/17=cos^(-1)""36/85.

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  18. Prove that cos^(-1)""(12)/(13)+cos^(-1)""(4)/(3)=tan^(-1)""(56)/(33)

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  19. Prove that : 2tan^(-1)(sqrt((a-b)/(a+b))tan""x/2)=cos^(-1)((acosx+b)/(...

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  20. Prove that tan^(-1)x+"tan"^(-1)(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3...

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