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If 2tan^(-1)x+sin^(-1)(2x)/(1+x^2) is in...

If `2tan^(-1)x+sin^(-1)(2x)/(1+x^2)` is independent of `x ,` then `x >1` (b) `x<-1` (c) `0

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To solve the problem, we need to analyze the expression given and determine under what conditions it is independent of \( x \). The expression is: \[ 2 \tan^{-1} x + \frac{\sin^{-1}(2x)}{1 + x^2} \] ...
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CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. Find tan^(-1)x/(sqrt(a^2-x^2)) in terms of sin^(-1) where x in (0, a)d...

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  2. If tan^(-1)(x^2+3|x|-4)+cot^(-1)(4pi+sin^(-1)sin 14)=pi/2, t h e n th...

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  3. If 2tan^(-1)x+sin^(-1)(2x)/(1+x^2) is independent of x , then x >1 (b...

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  4. Equation 1+x^2+2x"sin"(cos^(-1)y)=0 is satisfied by (a) exactly one ...

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  5. If the equation2^((2pi)/cos^(-1)x)-(a+1/2)2^((pi)/cos^(-1)x-a^2=0 has ...

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  6. Let alpha=som^(-1)((36)/(85)),beta=cos^(-1)(4/5)a n dgamma=tan^(-1)(8/...

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  7. If Sn=cot^(-1)(3)+cot^(-1)(7)+cot^(-1)(13)+cot^(-1)(21)+ddotn terms, ...

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  8. The value of tan[cos^(-1)(4/5)+tan^(-1)(2/3)] is 6/(17) (b) 7/(16) (...

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  9. If tan^(-1)(sqrt(1+x^2-1))/x=4^0 then x=tan2^0 (b) x=tan4^0 x=tan1/4...

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  10. The value of 2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x) is equal to (a...

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  11. The value of cot(sum(n=1)^2 cot^-1(1+sum(k=1)^n 2k)) is (a) 23/25 (b) ...

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  12. sin^(-1)(sin5)&gt; x^2-4x hold if (a) x=2-sqrt(9-2pi) (b) x=2+s...

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  13. The trigonometric equation sin^(-1)x=2sin^(-1)a has a solution for all...

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  14. If f(x)=x^(11)+x^9-x^7+x^3+1 and f(sin^(-1)(sin8))=alpha,alpha is cons...

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  15. If sin^(-1)x+sin^(-1)y=pi/2,t h e n(1+x^4+y^4)/(x^2-x^2y^2+y^2) is equ...

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  16. The value of (alpha^3)/2cos e c^2(1/2tan^(-1)alpha/beta)+(beta^3)/2sec...

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  17. There exists a positive real number of x satisfying "cos"(tan^(-1)x)=x...

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  18. The value of "tan"(sin^(-1)("cos"(sin^(-1)x)))"tan"(cos^(-1)(sin(cos^(...

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  19. The solution set of inequality (cot^(-1)x)(tan^(-1)x)+(2-pi/2)cot^(-1)...

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  20. If x=sin^(-1)(a^6+1)+cos^(-1)(a^4+1)-tan^(-1)(a^2+1),a in R , then th...

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