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Show that : tan^(-1)[(sqrt(1+x^(2))+sq...

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)`.

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

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

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

Prove that cot^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/(4)+(1)/(2)cos^(-1)x

Differentiate tan^-1{( sqrt (1+x^2) +sqrt (1-x^2))/ (sqrt(1+x^2)-sqrt(1-x^2))} w.r.t.x

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

If tan^(-1). (sqrt((1+x^(2))) - sqrt((1-x^(2))))/(sqrt((1+x^(2)))+sqrt((1-x^(2))))=alpha" , then " x^(2) is

f(x)=cos^(-1)(x^(2)/sqrt(1+x^(2)))

ACCURATE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTIONS CARRYING 4 MARKS
  1. Show that : tan^(-1)[(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sq...

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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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