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tan^(-1) 1+tan ^(-1) 2+tan ^(-1) 3 = p...

`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]

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

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

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

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

Evaluate : 4 (2 tan ^(-1)""(1)/(3)+tan ^(-1)""(1)/(7))

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

2 ( tan ^(-1)""(1)/(4) +tan ^(-1)""(2)/(9))=cos ^(-1)""(3)/(5)

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

tan^(-1)x+tan^(-1) (1-x) = 2 tan ^(-1) sqrt(x(1-x))

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

CHHAYA PUBLICATION-TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS-Long answer type questions
  1. 2 cot ^(-1) 5+cot ^(-1) 7 + 2 cot ^(-1) 8=(pi)/(4)

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  2. 4 tan ^(-1 )""(1)/(5) - tan ^(-1)""(1)/(239)=(pi)/(4)

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

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

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

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

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  7. 2 tan ^(-1) (sqrt((a-b)/(a+b))tan""(x)/(2))=cos^(-1)""(acos x+b)/(a+b ...

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

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

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

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  11. (1)/(2)cos ^(-1)""((5 cos x +3)/(5+3 cos x))= tan^(-1)""((1)/(2)tan "...

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

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

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

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

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

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

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

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

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  20. sin ^(-1) x+sin ^(-1) (1-x) = cos ^(-1) x

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