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prove tan ^(-1)((sqrt(1+x)-sqrt(1-x))/(s...

prove `tan ^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=pi/4-1/2 cos ^(-1) x, -1/2 le x le 1`

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V PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. prove that tan^(-1) sqrt x = 1/2 cos^(-1)((1-x)/(1+x)), x in [0,1]

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  2. Prove the following : cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sin...

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  3. prove tan ^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=pi/4-1/2 ...

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  4. Prove the following : (9pi)/8-9/4 sin^(-1)(1/3)=9/4 sin^(-1) ((2sqrt2...

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  5. Solve the following 2tan^-1(cosx)=tan^-1(2cosecx)

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  6. Solve the following : tan^(-1)((1-x)/(1+x))=1/2 tan^(-1) x (x gt0)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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