[1-(sin^2(x))(cos^2(x))/cos^ 4(x)=tan^4(x)+tan^2(x)+1 :?
J jas397 New member Joined Jan 1, 2006 Messages 13 Jan 2, 2006 #1 [1-(sin^2(x))(cos^2(x))/cos^ 4(x)=tan^4(x)+tan^2(x)+1 :?
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,216 Jan 2, 2006 #2 I'll get you started, then you finish. OK?. You have: 1−sin2xcos2xcos4x\displaystyle \frac{1-sin^{2}xcos^{2}x}{cos^{4}x}cos4x1−sin2xcos2x =1cos4x−sin2xcos2xcos4x\displaystyle \frac{1}{cos^{4}x}-\frac{sin^{2}xcos^{2}x}{cos^{4}x}cos4x1−cos4xsin2xcos2x =1cos4x−sin2xcos2x\displaystyle \frac{1}{cos^{4}x}-\frac{sin^{2}x}{cos^{2}x}cos4x1−cos2xsin2x Now, use the identities sinxcosx=tanx\displaystyle \frac{sinx}{cosx}=tanxcosxsinx=tanx and tan2x+1=1cos2x\displaystyle tan^{2}x+1=\frac{1}{cos^{2}x}tan2x+1=cos2x1 to finish.
I'll get you started, then you finish. OK?. You have: 1−sin2xcos2xcos4x\displaystyle \frac{1-sin^{2}xcos^{2}x}{cos^{4}x}cos4x1−sin2xcos2x =1cos4x−sin2xcos2xcos4x\displaystyle \frac{1}{cos^{4}x}-\frac{sin^{2}xcos^{2}x}{cos^{4}x}cos4x1−cos4xsin2xcos2x =1cos4x−sin2xcos2x\displaystyle \frac{1}{cos^{4}x}-\frac{sin^{2}x}{cos^{2}x}cos4x1−cos2xsin2x Now, use the identities sinxcosx=tanx\displaystyle \frac{sinx}{cosx}=tanxcosxsinx=tanx and tan2x+1=1cos2x\displaystyle tan^{2}x+1=\frac{1}{cos^{2}x}tan2x+1=cos2x1 to finish.
stapel Super Moderator Staff member Joined Feb 4, 2004 Messages 16,582 Jan 2, 2006 #3 Yo: what have YOU tried? jas397 said: [1-(sin^2(x))(cos^2(x))/cos^ 4(x)=tan^4(x)+tan^2(x)+1 Click to expand... You have an unmatched bracket at the beginning of your character string. Did galactus guess your meaning correctly? Please confirm or correct. When you reply, please show what you have done. Thank you. Eliz.
Yo: what have YOU tried? jas397 said: [1-(sin^2(x))(cos^2(x))/cos^ 4(x)=tan^4(x)+tan^2(x)+1 Click to expand... You have an unmatched bracket at the beginning of your character string. Did galactus guess your meaning correctly? Please confirm or correct. When you reply, please show what you have done. Thank you. Eliz.