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Prove that tan ^(-1) ((sqrt(1+x^2)+sqrt(...

Prove that `tan ^(-1) ((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2)))=pi/4+1/2 cos ^(-1) x^2`

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V PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. Solve the following : tan^(-1)((1-x)/(1+x))=1/2 tan^(-1) x (x gt0)

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  2. sin(tan^(-1)x),|x| lt1 is equal to

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  3. sin^(-1)(1-x)-2sin^(-1)x= pi/2,then find x

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  4. tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))=

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  5. Find the principal values cos ^(-1)((-sqrt3)/2 )

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  6. Find the principal values cosec^(-1)((-2))

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  7. Evaluate the following sin [pi/2-sin ^(-1)((-sqrt3)/2)]

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  8. If tan ^(-1)(3/4)=theta, find the value of sin theta

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  9. Prove that tan ^(-1) (1/7)+tan ^(-1)( (1)/(13))=tan ^(-1)( 2/9)

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  10. Prove that sin ^(-1) (4/5)+sin ^(-1) (5/(13))+sin ^(-1) ((16)/(65))=pi...

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  11. Prove that tan ^(-1) ((a-b)/(1+a b))+tan ^(-1)(( b-c)/(1+b c))+tan ^(-...

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  12. Prove that 2 tan ^(-1) (1/5)+sec ^(-1) ((5 sqrt2)/7)+2 tan ^(-1) (1/8)...

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  13. If cos ^-1 x+cos ^(-1) y+cos ^(-1) z=pi and 0ltx, y ,zlt1,show that x^...

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  14. If (-1)ltx, y, z le 1such that sin ^(-1) x+sin ^(-1) y+sin ^(-1) z=(3...

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  15. If tan^-1x+tan^-1y+tan^-1z=pi,show that x+y+z=xyz

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  16. Show that 'tan ^(-1) (m/n)-tan ^(-1) ((m-n)/(m+n))=pi/4'

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  17. Show that tan ^(-1) n+cot ^(-1)(n+1)=tan ^(-1)(n^2+n+1)

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  18. Prove that 2 tan ^(-1)[(sqrt((a-b)/(a+b))) tan ((theta)/2)]=cos ^(-1)(...

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  19. i) In which range is the inverse of sine defined? ii) What is the rang...

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  20. Prove that tan ^(-1) ((sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^...

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