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Prove the "sin"^(-1) sqrt((x-q)/(p-q))="...

Prove the `"sin"^(-1) sqrt((x-q)/(p-q))="cos"^(-1)`sqrt((p-x)/(p-q))="cot"^(-1) sqrt((p-x)/(x-q))`

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ARIHANT PRAKASHAN-INVERSE TRIGONOMETRIC FUNCTIONS -PRACTICE QUESTIONS (Exams., Textbook.s & Other Imp. Questions) (4 MARKS Questions)
  1. Solve for x, 2 tan ^(-1)(cos x) =tan^(-1) (2"cosec"x).

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  2. Prove that : "cos"^(-1) ((b+a "cos"x)/(a+b "cos"x)) =2"tan"^(-1)(sqr...

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  3. Prove the "sin"^(-1) sqrt((x-q)/(p-q))="cos"^(-1)sqrt((p-x)/(p-q))="co...

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

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  5. Prove statement "sin"^(-1) 3/5+ "cos"^(-1)12/13="cos"^(-1) 33/65

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  6. Prove that (9pi)/(8) -(9)/(4) sin^(-1)((1)/(3)) =(9)/(4) sin^(-1)((2sq...

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  7. Express the value of "tan"^(-1)(x/y)-"tan"^(-1)((x-y))/((x+y) in simpl...

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  8. Prove that tan^(-1)((1)/(5)) +tan^(-1)((1)/(7)) +tan^(-1)((1)/(3)) +...

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  9. Prove that cos(sin^(-1)((3)/(5)) +cot^(-1)((3)/(2))) =(6)/(5sqrt(13))

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  10. Prove the following: 2\ tan^(-1)(3/4)-tan^(-1)((17)/(31))=pi/4

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  11. Prove that : cot^(-1)7+cot^(-1)8+cot^(-1)18=cot^(-1)3

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  12. Solve for x: - tan^(-1)("x"+1)+tan^(-1)("x"-1)=tan^(-1) (8/31)

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  13. Solve the following for x : tan^(-1)2x+tan^(-1)3x=npi+(3pi)/4

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  14. Prove that: tan^(-1)[(sqrt(1+x)-sqrt(1-x))/(sqrt(1+)x+sqrt(1-x))]=pi/4...

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  15. Prove that cos^(-1)(x)+ cos^(-1){(x)/(2)+sqrt(3-3x^(2))/(2)}=(pi)/(3).

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  16. Prove that tan^(-1)((6x-8x^(3))/(1-12x^(2)))-tan^(-1)((4x)/(1-4x^(2)))...

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  17. Solve: 2sin^(-1) x +sin^(-1) (1-x)= pi/2

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  18. Prove that following cot^(-1)((xy+1)/(x-y)) +cot^(-1)((yz+1)/(y-z))+...

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  19. Prove that tan^(-1)((cosx)/(1+sin x)) =(pi)/(4)-(x)/(2), x in (-(pi...

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  20. Prove that tan^(-1)(1)+tan^(-1)(2) +tan^(-1)(3) =pi.

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