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tan ^(-1) ""sqrt(x) =(1)/(2) cos^(-1) ...

`tan ^(-1) ""sqrt(x) =(1)/(2) cos^(-1) ""(1-x)/(1+x) , 0 le x le 1`

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show that, tan^(-1) ((1)/(sqrt(3)) tan ""(x)/(2))=(1)/(2) cos^(-1) ""((1+2 cos x)/(2+ cos x)).

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CHHAYA PUBLICATION-TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS-Very short answer type Questions
  1. Express each of the following in terms of other inverse circular ...

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  2. tan ^(-1) "" (1)/(2) + tan ^(-1) "" (2)/(11) = tan ^(-1)""(3)/(4)

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  3. cos ^(-1)"" (1)/(sqrt(5))+ cos ^(-1) ""(2)/(sqrt(5))=(pi)/(2)

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  4. 2 tan ^(-1) ""(1)/(2) = tan^(-1) ""(4) /(3)

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  5. 2 tan ^(-1) ""(1)/(5)+tan^(-1)"" (1)/(8)= tan ^(-1) ""(4)/(7)

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  6. sin ^(-1) ""(3)/(5) + sin ^(-1)""(8)/(17) = sin ^(-1)""(77)/(85)

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  7. cos^(-1) ""(15)/(17) + cos ^(-1)""(3)/(5)= cos ^(-1) ""(13)/(85)

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  8. tan ^(-1)"" a+ cot ^(-1)""b=cot ^(-1) ""(b-a)/(1+ab)

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  9. 4(cot ^(-1)3+"cosec"^(-1) sqrt(5))=pi

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  10. sin ^(-1) "" (1)/(sqrt(5))+cot ^(-1) 3= (pi)/(4)

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  11. tan ^(-1) ""sqrt(x) =(1)/(2) cos^(-1) ""(1-x)/(1+x) , 0 le x le 1

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  12. sec^(2) ( tan ^(-1)3) + "coses"^(2) (cot ^(-1) 4) = 27

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  13. sec^(2) ( cot ^(-1) 2) + "cosec"^(2) (tan ^(-1)3)=2""(13)/(36)

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  14. if two angles of a triangle are tan ^(-1)""(1)/(2) and tan^(-1...

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  15. If two angles of a triangle are tan ^(-1) 2 and tan^(-1) 3, wha...

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  16. 2 sin ^(-1 ) x= cos ^(-1) x

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  17. tan ^(-1) ""(1)/(x)+tan ^(-1) ""2=(pi)/(2)

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  18. 2 tan ^(-1) ""(2x)/(1-x^(2))=(pi)/(3)

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  19. tan ^(-1) (cot x) + cot ^(-1) (tan x) =(pi)/(4)

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  20. tan ^(-1)""(1-x)/(1+x)-(1)/(2) tan ^(-1 )""x=0 where x gt 0

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