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cos^(-1)""(2)/(sqrt(5))+sin ^(-1)""(1)/(...

`cos^(-1)""(2)/(sqrt(5))+sin ^(-1)""(1)/(sqrt(10))=(pi)/(4)`

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cos ^(-1)"" (1)/(sqrt(5))+ cos ^(-1) ""(2)/(sqrt(5))=(pi)/(2)

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cos sin ^(-1)(-(sqrt(3))/(2))

The value of alpha such that sin^(-1)(2/(sqrt(5))),sin^(-1)(3/(sqrt(10))),sin^(-1)alpha are the angles of a triangle is

sin ^(-1) "" (1)/(sqrt(5))+cot ^(-1) 3= (pi)/(4)

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

The value of alpha such that sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),sin^(-1)alpha are the angles of a triangle is (-1)/(sqrt(2)) (b) 1/2 (c) 1/(sqrt(3)) (d) 1/(sqrt(2))

sin ^(-1)sqrt(3)x+sin ^(-1)x=(pi)/(2)

If (1)/(sqrt2) lt x lt 1 , then prove that cos^(-1) x + cos^(-1) ((x + sqrt(1 - x^(2)))/(sqrt2)) = (pi)/(4)

CHHAYA PUBLICATION-TRIGONOMETRIC INVERSE CIRCULAR FUNCTIONS-Short answer type questions
  1. 2 ( tan ^(-1)""(1)/(4) +tan ^(-1)""(2)/(9))=cos ^(-1)""(3)/(5)

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

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  3. cos^(-1)""(2)/(sqrt(5))+sin ^(-1)""(1)/(sqrt(10))=(pi)/(4)

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  4. 2sin ^(-1)""(3)/(5) +sin ^(-1) ""(7)/(25)=(pi)/(2)

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  5. tan ^(-1) ""(1)/(3) + tan^(-1)""(1)/(7)+tan ^(-1)""(1)/(5)+tan ^(-1)...

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

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  7. tan ^(-1)""(1)/(p+q)+tan ^(-1)""(q)/(p^(2)+pq+1)=cot^(-1)p

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  8. tan^(-1)""(3)/(2) +tan^(-1)""(6)/(5)=pi - tan^(-1)""(27)/(8)

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

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

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

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

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

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

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

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

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

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

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

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

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