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Cot^(-1){(sqrt(1-sinx)+sqrt(1+sinx))/(sq...

`Cot^(-1){(sqrt(1-sinx)+sqrt(1+sinx))/(sqrt(1-sinx)-sqrt(1+sinx))}=`

A

`pi-x/2`

B

`2pi-x`

C

`pi/2`

D

`2pi-x/2`

Text Solution

Verified by Experts

The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE 1
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  2. Prove that tan{(pi)/4 + 1/2 Cos^(-1)((a)/(b))}+tan{((pi)/4-1/2 Cos^(-1...

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  3. Cot^(-1){(sqrt(1-sinx)+sqrt(1+sinx))/(sqrt(1-sinx)-sqrt(1+sinx))}=

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  4. "Tan"^(-1)(a-b)/(1+ab)+"Tan"^(-1)(b-c)/(1+bc)+"Tan"^(-1)(c-a)/(1+ca)=

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  5. Id a,b,c are distinct non-zero real numbers having the same sign. Prov...

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

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  7. "Tan"^(-1)(yz)/(xsqrt(x^(2)+y^(2)+z^(2)))+"Tan"^(-1)(zx)/(ysqrt(x^(2)+...

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  8. "Tan"^(-1)(c(1)x-y)/(c(1)y+x)+"Tan"^(-1)(c(2)-c(1))/(1+c(2)c(1))+"Tan"...

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  9. If "Tan"^(-1)1/(1+2)+"Tan"^(-1)1/(1+(2)(3))+"Tan"^(-1)1/(1+(3)(4))+......

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  10. If a(1),a(2),a(3),....,a(n) is an A.P. with common difference d, then ...

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  11. If x^(2)+y^(2)+z^(2)=r^(2), then Tan^(-1)((xy)/(zr))+Tan^(-1)((yz)/(xr...

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

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  13. If 0lexle1/2, then Sin^(-1)x+Sin^(-1)(x/2-sqrt(3-3x^(2))/2)=

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  14. If 1/2lexle1 then Cos^(-1)x+Cos^(-1)(x/2-sqrt(3-3x^(2))/2)=

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  15. If y is infinite and tan^(-1)y=4tan^(-1)x then

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  16. If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi then x+y+z=

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  17. If Tan^(-1)x+Tan^(-1)y+Tan^(-1)z=pi//2 then 1 - xy - yz - zx =

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  18. If Cos^(-1)x+Cos^(-1)y+Cos^(-1)z=pi,"then "x^(2)+y^(2)+z^(2)+2xyz=

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  19. If Sin^(-1)x+Sin^(-1)y+Sin^(-1)z=pi//2,"then "x^(2)+y^(2)+z^(2)+2xyz=

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  20. If Sin^(-1)x+Sin^(-1)y+Sin^(-1)z=pi then prove that n xsqrt(1-x^(2))+y...

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