I was given a homework sheet to verify several identities, but I could not figure out these two problems. Can someone enlighten me. 1. cos 4x= 1-8sin²x cos²x 2. (sin³x - cos³x)/(sinx - cosx) = 1+sinxcosx
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1. cos 4x= 1-8sin²x cos²x Right Side = 1 - 2 (4sin²x cos²x) = 1 - 2 (2sin x . cos x)² = 1 - 2 (sin 2x)² = (1)- 2 sin² 2x = (sin² 2x + cos² 2x) -2sin² 2x = cos² 2x - sin² 2x = cos 4x 2. (sin³x - cos³x)/(sinx - cosx) = 1+sinxcosx Left side because
finish it. hint for the second one ...
ahh, I see now. Thank you guys.
from left: since we have: but why: simply we can approve it like this: and we know that: = 1 we replace it and: finally we simplifying it:
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