Question

Simplify and express your answer in terms of cos x, sin2 x + 2 cos2x​

Answer 1

Answer:

am having problems understanding how to verify this identity. I am quite sure that it is to be solved using the Pythagorean identities but, alas, I'm not seeing what might otherwise be obvious.

I need to verify the identity

cos2x−sin2x=2cos2x−1cos2⁡x−sin2⁡x=2cos2⁡x−1

Thank you for your help.

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askedNov 17 '14 at 13:01



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editedNov 17 '14 at 13:47



amWhy

1

You know that cos2x+sin2x=1cos2⁡x+sin2⁡x=1, then write sin2xsin2⁡x in terms of cos2xcos2⁡x, then substitute your expression in cos2x−sin2xcos2⁡x−sin2⁡x and simplify. – Hakim Nov 17 '14 at 13:02

find some way of getting rid sin2xsin2⁡x on the LHS. – John Joy Nov 17 '14 at 15:00 

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Yes, indeed, we can use the Pythagorean Identity:

cos2x+sin2x=1⟺sin2x=1−cos2x