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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

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

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

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

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

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

Differentiate y with respect to x, where [y= tan^-1 { sqrt(1+sin x) + sqrt(1- sin x)} / {sqrt (1+ sin x) - sqrt(1- sin x)}]

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OMEGA PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -Important Questions from Miscellaneous Exercise
  1. Prove that tan^(-1)""(1)/(2)+tan^(-1)""(2)/(11)=tan^(-1)""(3)/(4)

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  2. Prove that tan^(-1)""(2)/(11)+tan^(-1)""(7)/(24)=tan^(-1)""(1)/(2).

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  3. Express tan^(-1)((cosx)/(1-sinx)),-(pi)/(2)ltxlt(pi)/(2) in the simple...

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  4. Prove that tan^(-1) (1/5)+ tan^(-1) (1/7) + tan^(-1) (1/3) + tan^(-1) ...

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

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

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

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

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

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

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

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  12. Show that "sin"^(-1)(5/(13))+"cos"^(-1)(3/(5))="tan"^(-1)(63/(16)).

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

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  14. Prove that : "sin"^(-1)(2xsqrt(1-x^(2)))=2"cos"^(-1)x,1/(sqrt(2))lexle...

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

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  16. Express "tan"^(-1)(("cos"x-"sin"x)/("cos"x+"sin"x)),0ltxltpi in the si...

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  17. Prove that : "tan"^(-1)(1/(2))+"tan"^(-1)(1/(5))+"tan"^(-1)(1/(8))=p...

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  18. Prove the following : "cos"^(-1)(4/(5))+"cos"^(-1)(12/(13))="cos"^(-...

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  19. Express "tan"^(-1)x/(sqrt(a^(2)-x^(2))),|x|lta, in the simplest form.

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  20. Express "tan"^(-1)(sqrt(1+x^(2))-1)/(x),xne0 in simplest form.

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