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Tan^(-1)[(sqrt(1+sinx)-sqrt(1-sinx))/(sq...

`Tan^(-1)[(sqrt(1+sinx)-sqrt(1-sinx))/(sqrt(1+sinx)+sqrt(1-sinx))]=`

A

`x`

B

`x/2`

C

`(x^(2))/2`

D

`2x`

Text Solution

Verified by Experts

The correct Answer is:
B
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AAKASH SERIES-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE-II
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  2. "Tan"^(-1)(cosx)/(1+sinx)=

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  3. Tan^(-1)[(sqrt(1+sinx)-sqrt(1-sinx))/(sqrt(1+sinx)+sqrt(1-sinx))]=

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  4. tan[1/2cos^(-1)((sqrt(5))/3)]=

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  5. sin^(-1)(sqrt(2)sin theta)+sin^(-1)(sqrt(cos 2 theta))=

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  6. If u=tan^(-1)(1/(sqrt(cos 2 theta)))-tan^(-1)(sqrt(cos 2 theta)), then...

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  7. sin[cot^(-1){cos(tan^(-1)x)}]=

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  8. 2"tan"^(-1)1/5+"tan"^(-1)1/7+2"tan"^(-1)1/8=

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  9. "tan"^(-1)5/6+1/2"tan"^(-1)11/60=

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  10. "tan"^(-1)(5/12)+sin^(-1)(24/25)=cos^(-1)(x) implies x=

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  11. In DeltaABCif C is a right angle then tan^(-1)(a/(b+c))+tan^(-1)(b/(c+...

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  12. tan[tan^(-1)(1/(a+b))+tan^(-1)(b/(a^(2)+ab+1))]=

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  13. sin[cot^(-1)((2x)/(1-x^(2)))+cos^(-1)((1-x^(2))/(1+x^(2)))]=

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  14. IF 3 sin^(-1)((2x)/(1+x^(2)))-4cos^(-1)((1-x^(2))/(1+x^(2)))+ 2tan^(...

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  15. "tan"^(-1)1/3+"tan"^(-1)1/7+……+tan^(-1)(1/(n^(2)+n+1))=

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  16. Statement: I sin^(-1)x=x has only one solution Statement II: cos^(-1...

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  17. The ascending order of A=cos("sin"^(-1)12/13), B=sin(2"Tan"^(-1)3/4)...

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  18. If a,b,c, are positive then tan^(-1)sqrt((a(a+b+c))/(bc))+tan^(-1)sq...

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  19. If tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2)))=k tan^(-1)(x/a) then k=

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  20. If sec^(-1)(1/(sqrt(1-x^(2))))+cot^(-1)((sqrt(1-x^(2)))/x)=sin^(-1)(k)...

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