Best Answer

(1 + tanx)/sinx

Multiply by sinx/sinx

sinx + tanxsinx

Divide by sin2x (1/sin2x) = cscx

cscx + tan(x)csc(x)

tanx = sinx/cosx and cscx = 1/sinx

cscx + (sinx/cosx)(1/sinx)

sinx cancels out

cscx + 1/cosx

1/cosx = secx

cscx + secx

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โˆ™ 2011-03-02 03:27:13
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Q: Parenthesis 1 plus tanx end parenthesis divided by sinx equals cscx plus secx?
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Related questions

What is the integral of cscx?

- ln (cscx + cotx) + C You use u substitution.

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You could try y = 1/sin(x) but I do not see how that helps.

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pi divided by 6 is a constant and so its first derivative is 0. And since that is also a constant, the second derivative is 0. It is not clear what f(x) = csc(x) has to do with that!

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d/dx csc(x) = - csc(x) tan(x)

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sinx cscx = 1 is the same thing as sinx(1/sinx) = 1 which is the same as sinx/sinx = 1. This evaluates to 1=1, which is true.

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d/dx cscx = d/dx 1/sinx = d/dx (sinx)-1= -(sinx)-2 cosx = -cosx/sin2x = -1/sinx.cosx/sinx = -cscx cotx I suggest you copy this out onto paper so it is more clear. The / signs make it harder to see what is happening compared to horizontal divide lines.

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