P prasum Feb 2010 460 37 May 20, 2010 #1 how to integrate y=(1+sin2x)/(cosx+sinx)between x=0 and x=45(in degrees)
mr fantastic MHF Hall of Fame Dec 2007 16,948 6,768 Zeitgeist May 20, 2010 #2 prasum said: how to integrate y=(1+sin2x)/(cosx+sinx)between x=0 and x=45(in degrees) Click to expand... Prove the following identity: \(\displaystyle \frac{1 + \sin (2x)}{\cos (x) + \sin (x)} = \cos (x) + \sin (x)\). Now the integration is trivial.
prasum said: how to integrate y=(1+sin2x)/(cosx+sinx)between x=0 and x=45(in degrees) Click to expand... Prove the following identity: \(\displaystyle \frac{1 + \sin (2x)}{\cos (x) + \sin (x)} = \cos (x) + \sin (x)\). Now the integration is trivial.
P prasum Feb 2010 460 37 May 20, 2010 #3 thanks for the suggestion. please tell me how to prove the identity(Wink)
harish21 Feb 2010 1,036 386 Dirty South May 20, 2010 #4 prasum said: thanks for the suggestion. please tell me how to prove the identity(Wink) Click to expand... \(\displaystyle \frac{1+sin(2x)}{cosx+sinx} \times \frac{cosx+sinx}{cosx+sinx}\) Now simplify. I hope you know that sin2x = 2sinx.cosx
prasum said: thanks for the suggestion. please tell me how to prove the identity(Wink) Click to expand... \(\displaystyle \frac{1+sin(2x)}{cosx+sinx} \times \frac{cosx+sinx}{cosx+sinx}\) Now simplify. I hope you know that sin2x = 2sinx.cosx