Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Prove that ----1/2 (cos :2 theta-cos 8theta)=sin 5theta.sin 3theta​

Sagot :

victorcarlos346

Prove that:

[tex]cos(2\alpha )-cos(8\alpha )=sin(5\alpha )sin(3\alpha )[/tex]

Remember that:

[tex]cos(A+B)=cos(A)cos(B)-sin(A)sin(B)\\cos(A-B)=cos(A)cos(B)+sin(A)sin(B)\\\\\\cos(A+B)-cos(A-B)=-2sin(A)sin(B)[/tex]

We wish to remove this add (A+B).

[tex]\left \{ {{A+B=p} \atop {A-B=q}} \right. \\\\2A=p+q[/tex]

[tex]A=\frac{p+q}{2} \\\\B=\frac{p-q}{2}[/tex]

Then we de identity:

[tex]cos(p)-cos(q)=-2sin(\frac{p+q}{2}) sin(\frac{p-q}{2})[/tex]

Let p=2α and q=8α

[tex]cos(2\alpha )-cos(8\alpha )=-2sin(\frac{2\alpha +8\alpha }{2})sin(\frac{2\alpha -8\alpha }{2}) \\\\cos(2\alpha )-cos(8\alpha )=-2sin(5\alpha )sin(-3\alpha )\\\\*sin(-\alpha )=-sin(\alpha )\\\\cos(2\alpha )-cos(8\alpha )=2sin(5\alpha )sin(3\alpha )[/tex]

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.