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Simplify tan ^(-1)[(a cos x-b sin x)/(b ...

Simplify `tan ^(-1)[(a cos x-b sin x)/(b cos x+a sin x)]` if, `a/b tan xgt(-1)`

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V PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-QUESTION BANK
  1. show that sin^-1frac(3)(5)-sin^-1frac(8)(17)=cos^-1frac(84)(85)

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  2. Prove that sin^-1frac12(13)+cos^-1frac4(5)+tan^-1frac63(16)=pi

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  3. Simplify tan ^(-1)[(a cos x-b sin x)/(b cos x+a sin x)] if, a/b tan xg...

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  4. Solve tan^-1 2x+tan^-1 3x=pi/4

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  5. Find the value of the following cos^(-1)(cos frac(13pi)6)

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  6. tan ^(-1)(tan((7 pi)/6))=

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  7. Prove that 2 sin^-1(frac(3)(5))=tan^-1(frac(24)(7))

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  8. prove sin ^(-1) ((8)/17)+sin ^(-1)(( 3)/5)=tan ^(-1)(( 77)/(36))

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  9. prove cos ^(-1) (4/5)+cos ^(-1) ((12)/(13))=cos ^(-1) ((33)/(65))

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  10. Prove the following : cos^(-1)(12/13)+sin^(-1)(3/5)=sin^(-1)(56/65)

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  11. prove the following tan^(-1)frac(63)(16)=sin^(-1)frac(5)(13)+cos^(-1...

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  12. Show that tan^-1frac(1)(5)+tan^-1frac(1)(7)+tan^-1frac(1)(3)+tan^-1f...

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  13. prove that tan^(-1) sqrt x = 1/2 cos^(-1)((1-x)/(1+x)), x in [0,1]

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

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

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

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

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

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

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

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