SOLUTION: (sec2 2x - tan2 2x) / (sec 2x + tan 2x) = cos 2x / (1+ sin 2x)

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Question 1203075: (sec2 2x - tan2 2x) / (sec 2x + tan 2x) = cos 2x / (1+ sin 2x)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


manipulate left side

%28sec%5E2+%282x%29+-+tan%5E2+%282x%29%29+%2F+%28sec+%282x%29+%2B+tan+%282x%29%29 ...wririte using identities:sec%5E2+%282x%29+-+tan%5E2+%282x%29=1, sec+%282x%29+=1%2Fcos%282+x%29,+tan+%282x%29=sin%282+x%29%2Fcos%282+x%29

=1%2F+%28sec+%282x%29+%2B+tan+%282x%29%29 .......sec+%282x%29+%2B+tan+%282x%29=1%2Fcos%282+x%29+%2B+sin%282+x%29%2Fcos%282+x%29

=1%2F+%281%2Fcos%282+x%29+%2B+sin%282+x%29%2Fcos%282+x%29%29

=1%2F+%28%281%2B+sin%282+x%29%29%2Fcos%282+x%29%29

=cos%282+x%29%2F+%281%2B+sin%282+x%29%29