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Prove that tan^(-1)((cosx)/(1+sin x))...

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

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ARIHANT PRAKASHAN-INVERSE TRIGONOMETRIC FUNCTIONS -PRACTICE QUESTIONS (Exams., Textbook.s & Other Imp. Questions) (4 MARKS Questions)
  1. Prove that tan^(-1)((1)/(5)) +tan^(-1)((1)/(7)) +tan^(-1)((1)/(3)) +...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Prove that cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-...

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  15. Show that tan((1)/(2)"sin"^(-1)(3)/(4))=(4-sqrt(7))/(3).

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  16. Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2...

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

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  18. Prove that tan^(-1)sqrt(x) =(1)/(2) cos^(-1)((1-x)/(1+x)), x in (0, 1)...

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  19. Solve for x, cos (2sin^(-1)x)=(1)/(9), x gt 0.

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

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