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Prove that : cot^-1[(sqrt(1+sin x) + sqr...

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)`

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Differentiate w.r.t x : cot^-1{(sqrt (1+sin x) + sqrt (1-sin x))/(sqrt (1+sin x) - sqrt (1-sin x))}, 0 < x < pi/2

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

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OMEGA PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -Important Questions from Miscellaneous Exercise
  1. Prove that tan^(-1)""(1)/(5)+tan^(-1)""(1)/(7)+tan^(-1)""(1)/(3)+tan^(...

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  2. Show that sin^(-1)""(3)/(5)-sin^(-1)""(8)/(17)=cos^(-1)""(84)/(85)

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  3. Prove that : cot^-1[(sqrt(1+sin x) + sqrt(1-sin x))/(sqrt1+sin x + sqr...

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  4. Prove that (9pi)/(8)-9/(4)"sin"^(-1)1/(3)=9/(4)"sin"^(-1)(2sqrt(2))/(3...

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  5. Solve tan^(-1)(x+1)+tan^(-1)(x-1)=tan^(-1)""(8)/(31)

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  6. Prove that tan^(-1)sqrtx = 1/2cos^(-1) ((1-x)/(1+x)), x in [0,1]

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  7. Solve the 2 tan^-1 (cos x) = tan^-1 (2 cosec x).

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  8. Prove that 3cos^(-1)x=cos^(-1)(4x^(3)-3x),x in[(1)/(2),1]

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  9. Prove that sin^(-1)""(5)/(13)+cos^(-1)""(3)/(5)=sin^(-1)""(63)/(65)

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  10. Prove that : "tan"(pi/(4)+1/(2)"cos"^(-1)a/(b))+"tan"(pi/(4)-1/(2)"cos...

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  11. Prove that sin^(-1)(2x.sqrt(1-x^(2)))=2cos^(-1)x,(1)/(sqrt(2))lexlt1

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  12. Write in simplest form : "tan"^(-1)(sqrt((1-"cos"x)/(1+"cos"x))),xltpi...

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  13. Write the tan^-1 (frac{cos x - sin x}{cos x + sin x)), x < pi. in the ...

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  14. Prove that tan^(-1)""(1)/(2)+tan^(-1)""(1)/(5)+tan^(-1)""(1)/(8)=(pi...

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  15. Prove that : cos^-1 (4/5) + cos^-1(12/13) = cos^-1 (33/65)

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  16. Write tan^(-1)((x)/(sqrt(a^(2)-x^(2)))) in simplest form.

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  17. Write tan^(-1)((sqrt(1+x^(2))-1)/(x)),xne0 simplest form.

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  18. Find the value of cos^(-1)(cos""(13pi)/(6))

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  19. What is the principal value of "cos"^(-1)("cos"(2pi)/(3))+"sin"^(-1)("...

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  20. Prove that cos^(-1)""(12)/(13)+sin^(-1)""(3)/(5)=sin^(-1)""(56)/(65)

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