Verify the identity: a) \cos2x=\cos^{2}x-\sin^{2}x b) \cos2x=1-2\sin^{2}x

Mabel Breault 2021-12-18 Answered
Verify the identity:
a) cos2x=cos2xsin2x
b) cos2x=12sin2x
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Expert Answer

David Clayton
Answered 2021-12-19 Author has 36 answers
Step 1
Use cos(A+B)=cosAcosBsinAsinB
cos2x=cos(x+x)
=cosxcosxsinxsinx
=cos2xsin2x
Step 2
cosx=cos2xsin2x
=1sin2xsin2x
=12sin2x

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kalupunangh
Answered 2021-12-20 Author has 29 answers
Step 1
cos2x=cos2xsin2x
Lefty Side:
cos(A+B)=cosAcosBsinAsinB
cos2x=cos(x+x)
=cosxcosxsinxsinx
=cos2xsin2x
cos2x=cos2xsin2x
cos2x=cos(x+x)
=cosxcosxsinxsinx
=cos2xsin2x
(using pythagorian identity) cos2x=1sin2x
=1sin2xsin2x
=12sin2x

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