I need help justifying a quotient of two trig functions

Nh0

Feb 2019
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0
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I know (1-cos2(x/2))1/2/(1-cosx)1/2 Is equal to 1/root2 but I don't know a formal method for justifying this, so I'm asking for someone to show me how to show my teacher that it's a true identity
 

Debsta

MHF Helper
Oct 2009
1,293
592
Brisbane
I know (1-cos2(x/2))1/2/(1-cosx)1/2 Is equal to 1/root2 but I don't know a formal method for justifying this, so I'm asking for someone to show me how to show my teacher that it's a true identity
Work with the numerator first. Can you use one of the trig identities to simplify it into one term?

Now work with the denominator. Can you use a (different) trig identity to simplify it into one term?