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

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

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`2`
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tan ^(-1) ""(x-1)/(x-2) + tan ^(-1) ""(x+1)/(x+2)=(pi)/(4)

prove that tan ^(-1)"" (1)/(4) + tan ^(-1) ""(2)/(9) + tan ^(-1) "" (1)/(5) + tan ^(-1) ""(1)/(8) =(pi)/(4).

tan ^(-1) ""(1)/(3) + tan^(-1)""(1)/(7)+tan ^(-1)""(1)/(5)+tan ^(-1)""(1)/(8)=(pi)/(4)

Prove that tan ^(-1)""(1)/(x+y)+ tan ^(-1)""(y)/(x^(2)+xy+1)= cot ^(-1)x.

tan^(-1) 1+tan ^(-1) 2+tan ^(-1) 3 = pi =2 (tan ^(-1) ""(1)/(2)+tan ^(-1) ""(1)/(3) + tan ^(-1) 1) [ take priencipal value in each case]

If xy=1 + a^(2) then show that tan^(-1) ""(1)/(a+x)+tan ^(-1) ""(1)/(a+y)=tan ^(-1)""(1)/(a) , x+y+2a ne 0

solve : 3 tan ^(-1) ""(1)/(2+sqrt(3))-tan ^(-1)""(1)/(x) = tan ^(-1)""(1)/(3)

Show that , 4 (2 tan ^(-1) ""(1)/(3)+tan ^(-1)""(1)/(7)) =pi

prove that , 4 tan ^(-1) ""(1)/(5) -tan ^(-1 )""(1)/(70) + tan ^(-1) ""(1)/(99) = (pi)/(4) .

solve : tan ^(-1) 2x + tan ^(-1) ""3x=(pi)/(4)

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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