lilybugged
Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Prove the identity: cos(3x) + cos(x) = 2cos(2x)cos(x)
I'm almost done with my homework, just got stuck on this one.

Sagot :

kate200468
[tex]cos \alpha +cos \beta =2\cdot cos \frac{ \alpha + \beta }{2} \cdot cos \frac{ \alpha - \beta }{2}\\-----------------\\\\ \alpha =3x\ \ \ and\ \ \ \beta =x\\\\[/tex]

[tex]L=cos \alpha +cos \beta =cos(3x)+cos(x)\\\\\Rightarrow\ \ \ 2\cdot cos \frac{ \alpha + \beta }{2} \cdot cos \frac{ \alpha - \beta }{2}=2\cdot cos \frac{3x+x}{2} \cdot cos \frac{3x-x}{2} =\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =2\cdot cos \frac{4x}{2} \cdot cos \frac{2x}{2} =\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =2\cdot cos(2x)\cdot cos (x)=R[/tex]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.