SOLUTION: tan2x+sec2x=(sinx+cosx)^2/cos2x =========== =========== ========= Do you want to solve for x? Or prove it's an identity? Or just informing us?

Algebra ->  Trigonometry-basics -> SOLUTION: tan2x+sec2x=(sinx+cosx)^2/cos2x =========== =========== ========= Do you want to solve for x? Or prove it's an identity? Or just informing us?       Log On


   

Question 1183234: tan2x+sec2x=(sinx+cosx)^2/cos2x
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Do you want to solve for x?
Or prove it's an identity?
Or just informing us?


Found 4 solutions by MathLover1, MathTherapy, Alan3354, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

tan%282x%29%2Bsec%282x%29=%28sin%28x%29%2Bcos%28x%29%29%5E2%2Fcos%282x%29

Manipulating left side:

tan%282x%29%2Bsec%282x%29

=sin%282x%29%2Fcos%282x%29%2B1%2Fcos%282x%29

=%28sin%282x%29%2B1%29%2Fcos%282x%29.....1)

Manipulating right side:
%28sin%28x%29%2Bcos%28x%29%29%5E2=sin%5E2%28x%29%2B2sin%28x%29cos%28x%29%2B+cos%5E2%28x%29
%28sin%28x%29%2Bcos%28x%29%29%5E2=1%2B2sin%28x%29cos%28x%29...........2sin%28x%29cos%28x%29=sin%282x%29
%28sin%28x%29%2Bcos%28x%29%29%5E2=sin%282x%29%2B1

then go back to 1), left side is
=%28sin%28x%29%2Bcos%28x%29%29%5E2%2Fcos%282x%29


Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

tan2x+sec2x=(sinx+cosx)^2/cos2x
And what is your question? If you really need help.

Answer by Alan3354(69443) About Me  (Show Source):
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


tan%282x%29%2Bsec%282x%29

Put everything in terms of sine and cosine:

sin%282x%29%2Fcos%282x%29%2B1%2Fcos%282x%29+=+%28sin%282x%29%2B1%29%2Fcos%282x%29

Use sin(2x)=2sin(x)cos(x) and 1=sin^2(x)+cos^2(x):

%282sin%28x%29cos%28x%29%2Bsin%5E2%28x%29%2Bcos%5E2%28x%29%29%2Fcos%282x%29

Use (sin(x)+cos(x))^2 = sin^2(x)+2sin(x)cos(x)+cos^2(x):

%28sin%28x%29%2Bcos%28x%29%29%5E2%2Fcos%282x%29