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Prove that : cot^(-1) ((sqrt(1+x) -sq...

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

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

Prove that: tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}=pi/4-1/2 cos^(-1)x , 0

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

cot^(-1)(sqrt(1+x^2)-x)

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

Prove that cot^(-1) ((sqrt(1 + sin x) + sqrt(1 - sin x))/(sqrt(1 + sin x) - sqrt(1 - sin x))) = (x)/(2), x in (0, (pi)/(4))

Prove that: cot^(-1)((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))=(x)/(2),x in(0,(pi)/(4))

Prove that: cot^(-1)((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))=(x)/(2),x in(0,(pi)/(4))

cot^(-1)((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))=(x)/(2)

tan^(-1){(sqrt(1+cos x)+sqrt(1-cos x))/(sqrt(1+cos x)-sqrt(1-cos x))}

MODERN PUBLICATION-INVERSE - TRIGONOMETRIC FUNCTIONS-EXERCISE 2 (b) (Short Answer Type Questions)
  1. Solve the following equations : 2tan^(-1) (sin x) = tan^(-1) (2se...

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  2. Solve the following equations : cos (sin^(-1) x) = 1/2

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  3. Solve the following equations : tan^(-1) ((x-2)/(x-4)) +tan^(-1) (...

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  4. Solve for x , tan^(-1) ( x + 1) + tan^(-1) x + tan^(-1) ( x - 1) = t...

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  5. Solve for x : 3 sin^(-1) ((2x)/(1+x^(2))) - 4 cos^(-1) ((1-x^(2))...

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  6. Express each of the following in the simplest form: tan^(-1){(cosx)...

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  7. Write the following function in the simplest form: tan^(-1)((cosx-sinx...

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  8. Write the following function in the simplest form: tan^(-1)((cosx-sinx...

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  9. Write the following functions in the simplest form: tan^(-1){x/(a^2-x...

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  10. Write the following function in the simplest form: tan^(-1)(sqrt(1+x^2...

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  11. Write the following in the simplest form : tan ^(-1) ((sqrt(1-x^(...

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  12. Prove that : tan^(-1) ((sqrt(1-x^(2)))/(1+x)) = 1/2 cos^(-1) x

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  13. prove that 1/2tan^-1x=cos^-1xsqrt((1+sqrt(1+x^2))/(2sqrt(1+x^2))

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

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  15. tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))

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  16. Prove that : cot^(-1) ((sqrt(1+x) -sqrt(1-x))/(sqrt(1+x) +sqrt(1-x)...

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  17. cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2

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  18. If tan^(-1) x + tan^(-1) y - tan^(-1) z = 0 , then prove that : x...

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  19. If (i) cos^(-1) x + cos^(-1) y + cos^(-1) z = pi , prove that : x^...

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  20. Prove that: "sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^21)/(x^2+2)) ...

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