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

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

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The correct Answer is:
`"tan"^(-1)a/b-x`
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NCERT BANGLISH-INVERSE TRIGONOMETRIC FUNCTIONS-MISCELLANEOUS EXERCISE
  1. Simplify tan^(-1)[(a cos x -b sin x)/( b cos x +a sin x)] if a/b tan ...

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  2. Find the value of the following cos^(-1)("cos"(13pi)/6)

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  3. Find the value of the following tan^(-1)"tan"(7pi)/6

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  4. Prove That : 2"sin"^(-1)3/5="tan"^(-1)24/7

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  5. Prove That : "sin"^(-1)8/17+"sin"^(-1)3/5="tan"^(-1)77/36

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  6. Prove That : "cos"^(-1)4/5+"cos"^(-1)12/13="cos"^(-1)33/65

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  7. Prove That : "cos"^(-1)12/13+"sin"^(-1)3/5="sin"^(-1)56/65

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  8. Prove That : "tan"^(-1)63/16="sin"^(-1)5/13+"cos"^(-1)3/5

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

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  10. Prove That : tan^(-1)sqrt(x)=1/2"cos"^(-1)(1-x)/(1+x),x epsilon[0,1...

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  11. Prove That : cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqr...

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  12. Prove That : tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=...

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  13. Prove That : (9pi)/8-9/4"sin"^(-1)1/3=9/4"sin"^(-1)(2sqrt(2))/3

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  14. Solve the following equations : 2tan^(-1)(cosx)=tan^(-1)(2cosecx)

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  15. Solve the following equations : "tan"^(-1)(1-x)/(1+x)=1/2tan^(-1)x,(...

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  16. Solve the following equations : sin(tan^(-1)x),|x|lt1 equal to

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  17. Solve the following equations : sin^(-1)(1-x)-2sin^(-1)x=(pi)/2 the...

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  18. Solve the following equations : tan^(-1)(x/y)-"tan"^(-1)(x-y)/(x+y) ...

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