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

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  2. the value of 3tan^- 1(1/4)+tan^- 1(1/20)+tan^- 1(1/1985)

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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. Prove that : cot^(-1)((1+ab)/(a-b))+cot^(-1)((1+bc)/(b-c))+cot^(-1)((1...

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  5. Let cos^(-1)(x)+cos^(-1)(2x)+cos^(-1)(3x) = pi If x satisfies the equa...

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  6. If alpha=2 tan^(-1)((1+x)/(1-x)) and beta= sin^(-1)((1-x^2)/(1+x^2...

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  7. solve:sin^-1x+sin^-1 2x=pi/3

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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 for x : tan^(-1)(x-1)+tan^(-1)x+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 following equation: sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x

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

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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. Find the sum to n terms cot^(-1)(3)+cot^(-1)(7)+cot^(-1)(13)+ cot^(-1)...

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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. નીયેના બહુવિકલ્પ પ્રશ્નોના જ​વાબ માટે સાયો વિકલ્પ પસંદ કરો: sin^(-1...

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  18. tan^(-1)(m/n)+tan^(-1)((n-m)/(n+m))=?

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  19. Find the sum of the infinte series sin^(-1)(1/sqrt(2))+sin^(-1)((sqrt(...

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  20. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi, show that x^4+y^4+z^4+4x^2y^2z^2=...

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