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11/20/2019 5:07:11 PM
Posted: 10/20/2013 10:13:14 AM EST
[Last Edit: 10/20/2013 4:55:41 PM EST by chenault]
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Link Posted: 10/20/2013 10:43:44 AM EST
I think that I have number 1 can someone please check.


step 1) cosx/1+sinx (sin x is the same as 1+sin x so I multiply times the recipical 1-sin x)

step 2) cosx (1-sinx)/(1+sinx)(1-sinx) which breaks down into cosx(1-sinx)/(1-sinx^2)

step 3) because 1-sinx^2 is the same as 1+cos^2 I have 1+cos^2 which foiled out is (1+cos)(1+cos) so now my problem looks like thus cosx(1-sinx)/(1+cosx)(1+cosx)

step 4) the cosx on the numerator and denominator cancel out and I am left with (1-sinx)/(1+cosx) which is the same as (1/cosx) - (sinx/cosx) which equals (secx)-(tanx)

correct?
Link Posted: 10/20/2013 11:42:26 AM EST
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Originally Posted By chenault:
I think that I have number 1 can someone please check.


step 1) cosx/1+sinx (sin x is the same as 1+sin x so I multiply times the recipical 1-sin x)

step 2) cosx (1-sinx)/(1+sinx)(1-sinx) which breaks down into cosx(1-sinx)/(1-sinx^2)

step 3) because 1-sinx^2 is the same as 1+cos^2 I have 1+cos^2 which foiled out is (1+cos)(1+cos) so now my problem looks like thus cosx(1-sinx)/(1+cosx)(1+cosx)

step 4) the cosx on the numerator and denominator cancel out and I am left with (1-sinx)/(1+cosx) which is the same as (1/cosx) - (sinx/cosx) which equals (secx)-(tanx)

correct?
View Quote


No.

Your math has a series of errors. (1 + cos X)^2 does not = 1 + cos^2 x, but rather = 1 + 2 (cos x) + cos^2 x. Also, there is no cos x in the denominator to cancel out.

Solution:

Starting with the initial equation:

cosx/(1+sinx) = secx-tanx

rewrite everything in terms of cos and sin:

cos x / (1 + sin x) = (1 /cos x) - (sin x / cos x)

simplifying the right side becomes (1 - sin x)/ cos x

so:

cos x / (1 + sin x) = (1 - sin x) / cos x

multiply both sides by (cos x) (1 + sin x) to get the same denominators, and simplifying

gives us

cos x * cos x = (1 + sin x) (1 - sin x)

cos^2 x = 1 - sin^2 x

and then adding sin^2x to both sides

cos^2 x + sin^2 x = 1

since this is true, we prove the original equality.
Link Posted: 10/27/2013 4:27:43 AM EST
[Last Edit: 10/27/2013 4:29:22 AM EST by switchtanks]
wrong thread
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