Question 1172182: 1 + cot x/cot x -1 = 1 + sin 2x/cos 2x
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Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 1 + cot x/cot x -1 = 1 + sin 2x/cos 2x
(sin x+cos x)/sin x divided by (cos x-sin x)/sin x on the left
this is (sin x + cos x)/cos x-sin x)
multiply by conjugate of denominator, cos x+sin x, top and bottom
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sin ^x +cos ^2 x+ 2 sin x cos x is numerator , which is 1+ 2 sin x
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cos^2x- sin^2 x is the denominator, which is cos 2x
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The approach to this is to work on one side, by converting the cot to a cos/sin term.
When there is a term in the denominator that suggests that multiplying by a conjugate might work, do that and see what happens. sin x cos x is difficult to do much with, except that 2 sin x cos x= sin 2x, a very useful identity to know.
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