eah
Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Prove: cosx.cos2x+(sin2x)^ 2/2cosx=cosx

Sagot :

luana
[tex]cosx*cos2x+\frac{(sin2x)^2}{2cosx}=cosx\\\\ cosx*(cos^2x-sin^2x)+\frac{(2sinxcosx)^2}{2cosx}=cosx\\\\ cosx*(cos^2x-sin^2x)+\frac{4sin^2xcos^2x}{2cosx}=cosx\\\\ cosx*(cos^2x-sin^2x)+2sin^2xcosx=cosx\ \ \ |Divide\ by\ cosx\\\\ (cos^2x-sin^2x)+2sin^2x=1\\\\ cos^2x-sin^2x+2sin^2x=1\\\\ cos^2x+sin^2x=1\\\\ \boxed{1=1}\ \ TRUE[/tex]
[tex]cosxcos2x+\frac{sin^22x}{2cosx}=cosx\\\\L=cosx(cos^2x-sin^2x)+\frac{(2sinxcosx)^2}{2cosx}\\\\=cos^3x-sin^2xcosx+\frac{(2sinxcosx)^2}{2cosx}=\frac{2cosx(cos^3x-sin^2xcosx)+(2sinxcosx)^2}\\\\\\=\frac{2cos^4x-2sin^2xcos^2x+4sin^2xcos^2x}{2cosx}=\frac{2cos^2x(cos^2x+sin^2x)}{2cosx}\\\\=cosx\underbrace{(sin^2x+cos^2x)}_{use:sin^2x+cos^2x=1}=cosx=R\\\center\boxed{L=R}[/tex]


[tex]Other\ theorems:\\\\sin2x=2sinxcosx\\\\cos2x=cos^2x-sin^2x[/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.