Verifying trig. identities for Honors Pre Calc
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Multiply the left side by (1+cosx)/(1+cosx). FOIL out the numerator to get (1-cos^2x)/(sinx(1+cosx)). Using the Pythagorean Identity, 1-cos^2x=sin^2x. Therefore you have sin^2x/(sinx(1+cosx)). Cancel out a sine from the top and the bottom and you get sinx/(1+cosx). Then the left side equals the right side and you're good to go!
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First cross multiply:
(1-cos X)*(1+cos X) = sin^2 X
then multiply out the left side:
1 - cos^2 X = sin^2 X
add cos^2 X to both sides
1 = cos^2 X + sin^2 X
And that is the Pythagorean theorem
(1-cos X)*(1+cos X) = sin^2 X
then multiply out the left side:
1 - cos^2 X = sin^2 X
add cos^2 X to both sides
1 = cos^2 X + sin^2 X
And that is the Pythagorean theorem