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Prove that : tan^-1[(sqrt(1+z) + sqrt(1-...

Prove that : `tan^-1[(sqrt(1+z) + sqrt(1-z))/(sqrt(1+z) - sqrt(1-z))= pi/4 + 1/2 cos^-1z`

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Prove that : tan^-1[(sqrt(1+x^2) - sqrt(1-x^2))/(sqrt1+x^2 + sqrt(1-x^2))] = pi/4 - 1/2cos^-1x^2

Show that : tan^(-1)[(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))]=pi/4+1/2cos^(-1)x^(2) .

Prove that : tan^-1 [frac { (1+z)^(1/2) - (1-z)^(1/2)}{ (1+z)^(1/2) + (1-z)^(1/2)}]=frac{pi}{4}-frac{1}{2} cos^-1 (z) .

If sin^-1x + sin^-1y + sin^-1z = pi , prove that xsqrt(1-x^2)+y sqrt(1-y^2) + z sqrt(1-z^2) = 2xyz

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ACCURATE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTIONS CARRYING 4 MARKS
  1. Prove that : tan^-1[(sqrt(1+z) + sqrt(1-z))/(sqrt(1+z) - sqrt(1-z))= p...

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

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

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

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

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

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

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  8. Prove that cos (tan^(-1)(sin(cot^-1x))) =sqrt((x^2+1)/(x^2+2))

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

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

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

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

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

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

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

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

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

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

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

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

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

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