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sin^(-1) ""(2a)/(1+a^(2))-cos^(-1) ""(1-...

`sin^(-1) ""(2a)/(1+a^(2))-cos^(-1) ""(1-b^(2))/(1+b^(2))=2tan ^(-1) ""(a-b)/(1+ab)`

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

If sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x , then x is equal to [a , b , in (0,1)] (a) (a-b)/(1+a b) (b) b/(1+a b) (c) b/(1+a b) (d) (a+b)/(1-a b)

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

tan((1)/(2) sin ^(-1)""(2x)/(1+x^(2))+(1)/(2)cos^(-1)((1-x^(2))/(1+x^(2))))=(2x)/(1-x^(2))(|x|ne 1)

Prove that , a cos theta + b sin theta = sqrt(a^(2) +b^(2) ) cos ( theta - tan ^(-1) ""(b)/(a) ) =sqrt(a^(2) +b^(2)) sin (theta +tan ^(-1)""(a)/(b))

Find the value of : sin (sin ^(-1) ""(1)/(3) + sec ^(-1) 3)+cos( tan^(-1) ""(1)/(2) + tan ^(-1) 2)

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

If a,b,c are real positive numbers and theta =tan^(-1)[(a(a+b+c))/(bc)]^(1/2)+tan^(-1)[(b(a+b+c))/(ca)]^(1/2)+tan^(-1)[(c(a+b+c))/(ab)]^(1/2) , then tantheta equals

int_(0)^((pi)/(4))(dx)/(a^(2)cos^(2)x+b^(2)sin^(2)x)=(1)/(ab)tan^(-1).(b)/(a)(a,bge0)

prove that tan((pi)/(4)+(1)/(2) cos ^(-1)""(a) /(b) )+tan ((pi)/(4) -(1)/(2) cos ^(-1) ""(a)/(b))=(2b)/(a).

CHHAYA PUBLICATION-TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS-Short answer type questions
  1. tan ^(-1)x-tan ^(-1)y=sin ^(-1) ""(x-y)/(sqrt((1+x^(2))(1+y^(2)))

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

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

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  4. cot^(-1)""(xy+1)/(x-y)+cot^(-1)""(yz+1)/(y-z) +cot ^(-1) "" (zx +1)/(...

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  5. tan^(-1)""(x-y)/(1+xy)+tan^(-1)""(y-z)/(1+yz)+tan^(-1)""(z-x)/(1+zx) =...

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  6. cos^(-1)x= 2 sin ^(-1) sqrt((1-x)/(2))=2 cos ^(-1)""sqrt((1+x)/(2))=2t...

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  7. { cos (sin ^(-1) x)}^(2) ={sin (cos ^(-1) x)}^(2)

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  8. tan ^(1)(cotx) + cot ^(-1) (tan x)=pi -2x

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  9. tan^(-1) (cot x) +cot^(-1)(tan x) =pi -2x

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

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

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

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

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

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  15. 2 tan ^(-1)""(1+x)/(1-x)+sin ^(-1)""(1-x^(2))/(1+x^(2))

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

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

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

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

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

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