[From: ] [author: ] [Date: 11-05-18] [Hit: ]
(No teacher will give you credit for doing such a thing.If you work with the left and multiply and divide by 1 + sin(x),Next, use 1 - sin²(x) = cos²(x) and sec(x) = 1/cos(x).= sec(x)(1 + sin(x))/cos²(x) = (1/cos(x))(1 + sin(x))/cos²(x) = (1 + sin(x))/cos^3(x).Now multiply numerator and denominator with cos x.......
This is the problem:

secx/(1-sinx) = (1+sinx)/cos^3x

I've tried working through it several times, but for some reason, I'm just not getting it. I can't figure out how to make both sides equal.
Even if you were to only show me how to start it would help.
Thanks.

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You can not "cross multiply". That is an invalid move because it presumes that the statement is true. Your job is to prove it is true. (No teacher will give you credit for doing such a thing.)

If you work with the left and multiply and divide by 1 + sin(x), you get

sec(x)/(1 - sin(x)) = sec(x)(1 + sin(x))/(1 - sin²(x))

Next, use 1 - sin²(x) = cos²(x) and sec(x) = 1/cos(x).

sec(x)/(1 - sin(x)) = sec(x)(1 + sin(x))/(1 - sin²(x))

= sec(x)(1 + sin(x))/cos²(x) = (1/cos(x))(1 + sin(x))/cos²(x) = (1 + sin(x))/cos^3(x).

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cross multiply:
(1-sin x)(1+sin x) = sec x * cos^3 x
Factor and simply the sec x * cos^3 x = cos^2 x
1 - sin^2 x = cos^2 x
Move the sin^2 x to the right
1 = sin^2 x + cos^2 x
QED

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sec x / (1-sin x) = sec x (1+sin x) / (1-sin x)(1+sin x) = (sec x + tan x) / (1-sin^2 x)
= (sec x + tan x) / cos^2x
Now multiply numerator and denominator with cos x. You will get:
(1+sin x) / cos^3 x = answer

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secx/(1-sinx)=

(1/cosx)/(1-sinx)=

[-1/((sinx-1)*cosx)]*[(sinx+1)/(sinx+1…

-(1+sinx)/(-cos^3X)= (1+sinx)/cos^3x
1