SOLUTION: Can someone please explain to me with steps of simplifying this?thanks would be greatly appreciated. simplify 1.)sin3 theta+cos3theta divided by sintheta+costheta Verify t

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Question 753558: Can someone please explain to me with steps of simplifying this?thanks would be greatly appreciated.
simplify
1.)sin3 theta+cos3theta divided by sintheta+costheta

Verify the identies
1.)sectheta-costheta divided by tan theta =sin theta
2.)sintheta divided by 1+costheta+cottheta=csctheta
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
simplify
1.)sin3 theta+cos3theta divided by sintheta+costheta
(sin^3 + cos^3)/(sin+cos)
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= sin^2 - sin*cos + cos^2
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Verify the identies
1.)sectheta-costheta divided by tan theta = sin theta
[(1/cos)-cos] / [tan] = sin
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[(1-cos^2)/cos] = tan*sin
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cos*tan*sin = 1-cos^2
sin^2 = 1-cos^2
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True

2.)sintheta divided by 1+costheta+cottheta=csctheta
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sin/(1+cos) + cos/sin = 1/sin
----
sin^2/(1+cos) + cos = 1
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(1-cos^2)/(1+cos) + cos = 1
(1+cos) + cos = 1
2cos = 0
cos(x) = 0
True when x = 90 or x = 270 degrees
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Note: I think your post for Problem #2 needs some parentheses.
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Cheers,
Stan H.