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4 tan ^(-1 )""(1)/(5) - tan ^(-1)""(1)...

`4 tan ^(-1 )""(1)/(5) - tan ^(-1)""(1)/(239)=(pi)/(4) `

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

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

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

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

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

2 tan ^(-1)""(1)/(3) + sin ^(-1)""(4)/(5) =(pi)/(2)

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

Statement -I : tan ^(-1)""((3)/(4))+tan ^(-1) ""((1)/(7))= (pi)/(4) statement -II: "for" x gt 0 , y gt 0 tan^(-1 ) ((x)/(y))+tan^(-1)""((y-x)/(y+x))=(pi)/(4)

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

Prove that tan ^(-1)"" (4)/(3)+ tan ^(-1) "" (12)/(5) =pi - tan ^(-1) "" (56)/(33) .

CHHAYA PUBLICATION-TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS-Long answer type questions
  1. cot ^(-1) ""(1)/(2) -(1)/(2) cot^(-1)"" (4)/(3) =(pi)/(4)

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  2. 2 cot ^(-1) 5+cot ^(-1) 7 + 2 cot ^(-1) 8=(pi)/(4)

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  3. 4 tan ^(-1 )""(1)/(5) - tan ^(-1)""(1)/(239)=(pi)/(4)

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

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

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  6. cos^(-1)""(3)/(5) +cos ^(-1) "" (12)/(13) +cos ^(-1) "" (63)/(65)=(pi)...

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  7. tan^(-1) ""((1)/(2)tan 2A)+tan ^(-1)(cotA)+tan^(-1)(cot^(3)A) ={{:(0"...

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  8. 2 tan ^(-1) (sqrt((a-b)/(a+b))tan""(x)/(2))=cos^(-1)""(acos x+b)/(a+b ...

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  9. tan ( 2 tan ^(-1)sqrt((1+cos theta)/(1-cos theta)))+ tan theta =0

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  10. tan ^(-1) ""{(sqrt(1+cos x)+sqrt(1-cos x)}/{sqrt(1+cosx)-sqrt(1-cos x)...

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  11. cos ^(-1) ""((cos x + cos y)/(1+cos x cos y))= 2 tan ^(-1) (tan ...

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  12. (1)/(2)cos ^(-1)""((5 cos x +3)/(5+3 cos x))= tan^(-1)""((1)/(2)tan "...

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  13. tan ^(-1)""(1-x)/(1+x)- tan ^(-1 )""(1-y)/(1+y) = sin ^(-1) ""(y-x)/(...

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  14. If cos ^(-1) x+ cos ^(-1) y= theta , show that x^(2)-2xycos thet...

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  15. If sin ( pi cos theta ) = cos (pi sin theta ), , then sho...

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  16. Prove that , a cos theta + b sin theta = sqrt(a^(2) +b^(2) ) cos ...

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  17. IF 2 cos 4 theta + 9 cos 2 theta -7=0 , then show that , theta ...

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  18. cot ^(-1)""x+cot^(-1)""2x=(3pi)/(4)

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  19. cot ^(-1)x+cot^(-1)(a^(2)-x+1)=cot ^(-1)(a-1)

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  20. tan ^(-1)""(1-x)/(1+x)""=(1)/(2) sin ^(-1)""(x)/(sqrt(1+x^(2)))

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