SOLUTION: Prove the following identity 2/1+cosx - tan^2 x/2 = 1

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Question 821540: Prove the following identity
2/1+cosx - tan^2 x/2 = 1

Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!

There are three variations of tan((1/2)x):Since our tan is squared, I'm going to use the first one (and, since we're squaring it, the + is not needed):

Simplifying:

Changing the subtraction between the fractions into an equivalent addition (since this situation is a source of much confusion and many errors):

which simplifies to:

The denominators are equal so we can add the fractions:

And since the numerator and denominator are the same:

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