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Prove that cos[Tan^(-1){sin(Cot^(-1)x)}]...

Prove that `cos[Tan^(-1){sin(Cot^(-1)x)}] = sqrt((x^(2)+1)/(x^(2)+2))`

A

`((x^(2)+2)/(x^(2)+3))^(1//2)`

B

`((x^(3)+3)/(x^(2)+4))^(1//2)`

C

`((x^(2)+1)/(x^(2)+2))^(1//2)`

D

x

Text Solution

Verified by Experts

The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE 1
  1. tan(Cos^(-1)x)=

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  2. sin(Cot^(-1)(cos(Tan^(-1)x)))=

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  3. Prove that cos[Tan^(-1){sin(Cot^(-1)x)}] = sqrt((x^(2)+1)/(x^(2)+2))

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  4. 2Tan^(-1)(cosx)=

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  5. tan(2Tan^(-1)(sinx))=

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  6. Tan^(-1)(cotx)-Tan^(-1)(cot2x)=

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  7. 2Tan^(-1)((sqrt(a-b))/(a+b)"tan"x/2)=

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  8. tan[1/2"Sin"^(-1)(2a)/(1+a^(2))+1/2"Cos"^(-1)(1-a^(2))/(1+a^(2))]=

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  9. tan[1/2Sin^(-1)((2x)/(1+x^(2)))-1/2Cos^(-1)((1-y^(2))/(1+y^(2)))]=

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  10. Prove that sin[Cot^(-1) (2x)/(1-x^2)+Cos^(-1)((1-x^(2))/(1+x^(2)))]=1.

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  11. The value of tan[Tan^(-1)(1/(a+b))+Tan^(-1)(b/(a^(2)+ab+1))] is

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  12. Prove that tan{(pi)/4 + 1/2 Cos^(-1)((a)/(b))}+tan{((pi)/4-1/2 Cos^(-1...

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

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

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

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

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

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

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

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