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Need Help With Trig Problem?
the original problem is Verify: sin 2(theta)/1-cos2(theta) = cot(theta)
i keep on getting to the part where sin(squared)2(theta)=cos(theta)-cos(squared)2(theta) but im stuck after that. if you can please help
thanks
Just for ease of typing, let's use x instead of theta.
We start with sin 2x / ( 1 - cos 2x ). First we'll need to use both double angle identities to simplify these. Recall that:
sin 2x = 2 sin x cos x
For cos 2x, however, remember there are three choices. The best choice in this case turns out to be: cos 2x = 1 - 2 sin^2 x
Substituting each of those into the expression, this yields:
2 sin x cos x / ( 1 - ( 1 - 2 sin^2 x ) )
We can simplify the denominator by canceling the 1s. Now:
2 sin x cos x / 2 sin^2 x
From here, we can see both coefficients cancel, the 2s, and a sin x will cancel from top and bottom as well. Then we have:
cos x / sin x
Which then is equal to cot x.
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