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embizze eNotes educator| Certified Educator

We want to prove `sin8A=8sinA*cosA*cos2A*cos4A`


`=sin4Acos4A+sin4A+cos4A` :sum of angles identity


`=2(2sin2Acos2Acos4A)` ``: double angle identity


`=4(2sinAcosAcos2Acos4A)` : double angle identity

`=8sinAcosAcos2Acos4A` as required.

** In general, when proving trigonometric identities you start with one side, and by using allowable algebraic manipulations and other trigonometric identities, you transform that side into the other side.