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Prove that t a n^(-1)((cosx)/(1+sinx))=p...

Prove that `t a n^(-1)((cosx)/(1+sinx))=pi/4-x/2,\ x in (-pi/2,pi/2)`

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MODERN PUBLICATION-INVERSE - TRIGONOMETRIC FUNCTIONS-Frequently Asked Questions
  1. Find the value of : sin^() (2 tan^(-1). 1/4) +cos (tan^(-1)2sqrt(2))

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  6. Prove that tan[pi/4+1/2cos^(-1)""a/b]+tan[pi/4-1/2cos^(-1)""a/b]=2b/a

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  7. (9pi)/(8)-(9)/(4)sin^(-1)""(1)/(3)=(9)/(4)sin^(-1)""(2sqrt(2))/(3) (...

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

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  9. Prove that tan ^(-1) . 1/5 + tan^(-1) . 1/7 + tan ^(-1) . 1/8 = pi/4

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  10. Solve : 2 tan^(-1), (cos x) = tan^(-1), (2 cosec x)

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  11. Solve : tan^(-1) 4x +tan^(-1)6x = pi/4

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  12. If tan^-1 ((x-3)/(x-4))+tan^-1((x+3)/(x+4))=pi/4,

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  13. Solve : (i)" "tan^(-1). x/2 +tan^(-1). x/3 = pi/4 , sqrt(6) gt x gt 0...

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  14. If (tan^(-1)x)^2+(cot^(-1)x)^2=(5pi^2)/8, then find xdot

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  15. Prove that t a n^(-1)((cosx)/(1+sinx))=pi/4-x/2,\ x in (-pi/2,pi/2)

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  16. Express sin^(-1)((sin x+ cos x)/(2)), where -(pi)/(4) lt x lt (pi)/(4)...

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  17. Prove that : tan^(-1)x +tan^(-1). (2x)/(1-x^(2)) = tan^(-1) . (3x-x^(...

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  18. Simplify tan^(-1)[(acosx-bsinx)/(bcosx+asinx)], if a/btanx >-1 .

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

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  20. Prove the following: "cos"[tan^(-1){sin(cos t^(-1)x)}]= sqrt((1+x^2)/...

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