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Prove that: tan^(-1)x+tan^(-1)(1/x)={pi/...

Prove that: `tan^(-1)x+tan^(-1)(1/x)={pi/2,ifx >0-pi/2,ifx<0`

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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. 2"tan"(tan^(-1)(x)+tan^(-1)(x^3)),where x in R-{-1,1}, is equal to

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  2. If alpha=3sin^-1(6/(11)) and beta=3cos^-1(4/9), where the inverse trig...

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  3. Prove that: tan^(-1)x+tan^(-1)(1/x)={pi/2,ifx >0-pi/2,ifx<0

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  4. Find the value of sin^(-1)x+sin^(-1)(1/x)+cos^(-1)x+cos^(-1)(1/x)dot

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  5. Find the value of underset(r = 1)overset(10)sum underset(s = 1)overset...

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  6. If sin^(-1)xi in [0,1]AAi=1,2,3, .28 then find the maximum value of s...

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  7. Prove that cos^(-1)4/5 + cos^(-1)(12)/(13)=cos^(-1)(33)/(65)

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  8. If two angles of a triangle are tan^(-1)(2)a n dtan^(-1)(3), then find...

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  9. Find the sum of the following AP : 0.6, 1.7, 2.8, ……, to 100 terms.

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  10. Find the sum of the following AP -37, -33, -29, …… to 12 terms.

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  11. Let (x , y) be such that sin^(-1)(a x)+cos^(-1)(y)+cos^(-1)(b x y)=pi/...

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  12. Match the statements/expressions given in Column I with the values giv...

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  13. sum(r=1)^nsin^(-1)((sqrt(r)-sqrt(r-1))/(sqrt(r(r+1))))is equal to (a...

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  14. Prove that: sum(m=1)^ntan^(-1)((2m)/(m^4+m^2+2))=tan^(-1)((n^2+n)/(n^2...

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  15. The greater of the two angles A=2tan^(-1)(2sqrt(2)-1) and B=3sin^(-1)(...

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  16. The numerical value of "tan"(2tan^(-1)(1/5)+pi/4) is equal to

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  17. The value of alpha such that sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),...

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  18. The number of solutions of the equation tan^(-1)(1+x)+tan^(-1)(1-x)=pi...

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  19. Find the sum of given below: 34 + 32 + 30 + … + 10

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  20. If x , y , z are natural numbers such that cot^(-1)x+cot^(-1)y=cot^(-1...

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