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

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

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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

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

Prove that : cot^-1[(sqrt(1+sin x) + sqrt(1-sin x))/(sqrt1+sin x + sqrt(1-sin x))] = x/2, x in (0, pi/4)

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

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) .

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 2 tan^-1 sqrt((1- x)/(1+x))= x, -1 le x le 1

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

PRADEEP PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. Prove that : tan^-1[(sqrt(1+x) - sqrt(1-x))/(sqrt1+x + sqrt1-x)] = pi/...

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  2. Find the value of sin^-1(1/2)

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  3. Find the principal value of sin^-1(1/sqrt2)

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  4. Find the value of sin^-1(-1)

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  5. Find the value of sin^-1(-(1/2))

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  6. Find the principal value of cos^-1(sqrt3/2)

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  7. Find the value of cos^-1(-sqrt3/2)

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  8. Find the value of cos^-1(-1)

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  9. Find the principal value ofcos^-1(-1/sqrt2)

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  10. Find the value of sin(sin^-1 x + cos^-1 x ), |x| le 1

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  11. Find the value of sin^-1(sin(0pi/10))

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  12. Find the value of cos^-1(sqrt3/2) + 2 sin^-1(sqrt3/2)

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  13. Find the value of sin^-1[cos(sin^-1(sqrt3/2))]

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  14. Prove that following : 2 sin^-1 x = cos^-1 (1-2x^2), 0 le x le 1

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  15. Prove the following: 3sin^–1 x = sin^–1 (3x – 4x^3), x in [–1/2 , 1/2]

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  16. Prove the following: 3cos^–1 x = cos^–1 (4x^3 – 3x), x in [1/2,1]

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  17. Prove that following : cos^-1 x = 2 sin^-1 sqrt(1-x)/(2) = 2cos^-1 s...

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  18. Prove that following : sin(2 cos^-1(-4/5)) = - (24/25)

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  19. Prove that following : cos(2sin^-1(-2/5)) = 17/25

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  20. Prove that following : cos(3cos^-1(2/5)) = - (118)/(125)

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  21. Write the following functions in the simplest form: sin^-1 sqrt(1-x^...

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