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If sin^2x + sin^2y < 1 ; x, y in R then...

If `sin^2x + sin^2y < 1 ; x, y in R` then prove that `sin^-1(tanx . tany) in (-pi/2, pi/2)`.

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ALLEN-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. cos^(- 1)x=2sin^(- 1)sqrt((1-x)/2)=2cos^(- 1)sqrt((1+x)/2)

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  2. Prove: tan^(-1)2/3=1/2tan^(-1)(12)/5

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  3. If sin^2x + sin^2y < 1 ; x, y in R then prove that sin^-1(tanx . tany...

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  4. If a > b > c >0 , prove that cot^(-1)((a b+1)/(a-b))+cot^(-1)((b c+1)...

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  5. Let cos^(-1) (x) + cos^(-1) (2x) + cos^(-1) (3x) " be " pi. If x satis...

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  6. If alpha=2 arc t a n((1+x)/(1-x)) in B=a r c s i n((1-x^2)/(1+x^2))...

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  7. Solve the following: sin^(-1)x+sin^(-1)2x=pi/3 (ii) cos^(-1)x+sin^(-1)...

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  8. Arithmetic mean of the non-zero solutions of the equation tan^-1 (1/(2...

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  9. Solve: tan^(-1) x + tan^(-1)(x+ 1) + tan^(-1) (x-1) = tan ^(-1) 3x

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  10. Solve sin^(-1)x-cos^(-1)x=sin^(-1)(3x-2)

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  11. Solve the equation sin^(1) x + sin ^(-1) (1-x) = cos^(-1) x.

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  12. If tan^(- 1)((2x)/(x^2-1))+cos^(- 1){(x^2-1)/(x^2+1)}=(2pi)/3 then ...

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  13. Find the sum of the series :tan^- 1(1/3)+tan^- 1(2/9)+....+tan^- 1((2^...

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  14. Prove that cot^(-1)(13)+cos^(-1)(21)+cot^(-1)(-8)=pi.

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  15. Find the sum of each of the following series :(i) tan^-1(1/(x^2+x+1))+...

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  16. Find the domain of definition the following function: f(x)=log(10)(1-l...

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  17. Simplify : tan ^(−1)(1/2)+tan ^(−1) (1/3).

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  18. Prove that the identities, sin^-1 cos(sin^-1x)+cos^-1 sin(cos^-1x)=pi...

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  19. Prove that:tan^(-1)(m/n)+tan^(-1)((n-m)/(n+m))=pi/4

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  20. Find the sum of infinite series s = sin^(-1) ( 1/sqrt2) + sin ^(-1) ...

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