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sin cot^(-1)cos (tan ^(-1)x)=sqrt((x^(2...

`sin cot^(-1)cos (tan ^(-1)x)=sqrt((x^(2)+1)/(x^(2)+2))(x gt 0)`

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sin cos ^(-1) tan (sec^(-1) x) = sqrt(2-x^(2))

prove that cos tan ^(-1) ""sin cot ^(-1) ""x=((x^(2)+1)/(x^(2)+2))^(1/2)

Show that sin (cot^(-1) (tan cos^(-1)x)) =x

sin^(-1)x+sin^(-1)y=cos^(-1)""{sqrt((1-x^(2))(1-y^(2)))-xy}

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

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

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

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CHHAYA PUBLICATION-TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS-Short answer type questions
  1. sin cos ^(-1) tan (sec^(-1) x) = sqrt(2-x^(2))

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  2. sin "cosec"^(-1) cot (tan^(-1)x) =x

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  3. sin cot^(-1)cos (tan ^(-1)x)=sqrt((x^(2)+1)/(x^(2)+2))(x gt 0)

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  4. tan [(1)/(2) sin^(-1)""(2x)/(1+x^(2))+(1)/(2) cos ^(-1)""(1-y^(2))/(1...

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  5. cos (2cos ^(-1) x+sin ^(-1) x) , " when " x=(1)/(5) where 0 le ...

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  6. 2 tan ^(-1)""(1+x)/(1-x)+sin ^(-1)""(1-x^(2))/(1+x^(2))

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  7. tan (sin ^(-1)x+sin ^(-1) y) +tan (cos^(-1)x+cos ^(-1)y)

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  8. If xy=1 + a^(2) then show that tan^(-1) ""(1)/(a+x)+tan ^(-1) ...

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  9. "If " tan^(-1) x+ tan^(-1) y+tan ^(-1)z=(pi)/(2) , show that , x...

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  10. if tan ^(-1) x+tan ^(-1) y+tan ^(-1) z=pi prove that x+y+z=xyz

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  11. if cos^(-1)x+cos ^(-1)y+cos^(-1) z=pi prove that x^(2) +y^(2)+z...

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  12. "if " sin^(-1) x +sin ^(-1) y+sin ^(-1) z=pi show that , x^(4)+y...

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  13. IF cos (alpha +beta )=(5)/(13) and cos (alpha - beta )=(4)/(5), t...

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  14. If tan ^(-1) y= 4 tan ^(-1) x , find the algebric relation bet...

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  15. If tan ^(-1)x , tan ^(-1) y and tan^(-1) z are in A.P find t...

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  16. tan ^(-1) (x+1) + tan^(-1) (x-1) = tan ^(-1)"" (8)/(31)

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  17. tan (cos ^(-1) x) = sin (cot ^(-1) ""(1)/(2))

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  18. tan ^(-1)((1)/(2) sec x) + cot^(-1)(2cos x) =(pi)/(3)

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  19. sin ^(-1) ""(2a)/(1+a^(2))+sin ^(-1) ""(2b)/(1+b^(2) ) = 2 tan ^(-1...

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

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