SOLUTION: Hoping someone will help me with a few more. I need to see the steps:) Verify: a)sinx(sinx+cscxcos^2x)=1 b)tanx((cotx/cosx)-sinx)=cosx c)(1+cosx)(1-cosx)=sin^2x

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Question 269123: Hoping someone will help me with a few more. I need to see the steps:)
Verify:
a)sinx(sinx+cscxcos^2x)=1
b)tanx((cotx/cosx)-sinx)=cosx
c)(1+cosx)(1-cosx)=sin^2x
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Verify:
a)sinx(sinx+cscxcos^2x)=1
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sin^2(x) + (1)cos^2(x) = 1
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sin^2(x) + cos^2(x) is always 1, so you get:
1 = 1
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b)tanx((cotx/cosx)-sinx)=cosx
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tan(x)[(1/tan(x))/cos(x) - sin(x)) = cos(x)
---
(1/cos(x) - sin(x) = cos(x)
Multiply thru by cos(x) to get:
1 - cos(x)sin(x) = cos^2(x)
This is not an identity.
The left side of the original eq. does not equal the right side.
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c)(1+cosx)(1-cosx)=sin^2x
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1-cos^2(x) = sin^2(x)
sin^2(x) = sin^2(x)
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Cheers,
Stan H.