Answered

IDNLearn.com is designed to help you find the answers you need quickly and easily. Get the information you need from our community of experts who provide accurate and thorough answers to all your questions.

prove that [tex]cos 3 x =4 cos ^{3}x-3 cos x[/tex]

Sagot :

[tex]cos3x=4cos^3x-3cosx\\\\L=cos(2x+x)=cos2xcosx-sin2xsinx\\\\=(cos^2x-sin^2x)cosx-2sinxcosxsinx\\\\=cos^3x-sin^2xcosx-2sin^2xcosx\\\\=cos^3x-3sin^2xcosx\\\\=cos^3x-3cosx(1-cos^2x)\\\\=cos^3x-3cosx+3cos^3x\\\\=4cos^3x-3cosx=R[/tex]


[tex]cos(a+b)=cosa\ cosb-sina\ sinb\\\\sin^2a+cos^2b=1\to sin^2a=1-cos^2b\\\\cos2a=cos^2a-sin^2a\\\\sin2a=2sina\ cosa[/tex]
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.