How do I simplify the given equation? sin 3x cos 2x - cos 3x sin 2x Thank you
Z zee New member Joined Jan 15, 2006 Messages 8 Apr 15, 2006 #1 How do I simplify the given equation? sin 3x cos 2x - cos 3x sin 2x Thank you
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Apr 15, 2006 #2 Hello, zee! How do I simplify the given equation expression ?\displaystyle \text{How do I simplify the given }\sout{equation}\text{ expression ?}How do I simplify the given equation expression ? sin3x⋅cos2x − cos3x⋅sin2x\displaystyle \;\;\;\sin3x\cdot\cos2x\,-\,cos3x\cdot\sin2xsin3x⋅cos2x−cos3x⋅sin2x Click to expand... The quickest way is to recognize the compound-angle formula: sin(A − B) = sin(A)⋅cos(B) − cos(A)⋅sin(B)\displaystyle \;\;\sin(A\,-\,B)\;=\;\sin(A)\cdot\cos(B)\,-\,\cos(A)\cdot\sin(B)sin(A−B)=sin(A)⋅cos(B)−cos(A)⋅sin(B) We are given the right side of the formula with: A = 3x, B = 2x\displaystyle \,A\,=\,3x,\;B\,=\,2xA=3x,B=2x Answer: sin(A − B) = sin(3x − 2x) = sinx\displaystyle \,\sin(A\,-\,B)\;=\;\sin(3x\,-\,2x)\;=\;\sin xsin(A−B)=sin(3x−2x)=sinx
Hello, zee! How do I simplify the given equation expression ?\displaystyle \text{How do I simplify the given }\sout{equation}\text{ expression ?}How do I simplify the given equation expression ? sin3x⋅cos2x − cos3x⋅sin2x\displaystyle \;\;\;\sin3x\cdot\cos2x\,-\,cos3x\cdot\sin2xsin3x⋅cos2x−cos3x⋅sin2x Click to expand... The quickest way is to recognize the compound-angle formula: sin(A − B) = sin(A)⋅cos(B) − cos(A)⋅sin(B)\displaystyle \;\;\sin(A\,-\,B)\;=\;\sin(A)\cdot\cos(B)\,-\,\cos(A)\cdot\sin(B)sin(A−B)=sin(A)⋅cos(B)−cos(A)⋅sin(B) We are given the right side of the formula with: A = 3x, B = 2x\displaystyle \,A\,=\,3x,\;B\,=\,2xA=3x,B=2x Answer: sin(A − B) = sin(3x − 2x) = sinx\displaystyle \,\sin(A\,-\,B)\;=\;\sin(3x\,-\,2x)\;=\;\sin xsin(A−B)=sin(3x−2x)=sinx
K klt643 New member Joined Apr 14, 2006 Messages 7 Apr 15, 2006 #3 Hey- for this one you should use the trigonometric sum and difference identiy: Sin(x-y) = sinxcosy - sinycosx therefore, if you have sin3xcos2x - cos3xsin2x, it can be simplified into the above equation.
Hey- for this one you should use the trigonometric sum and difference identiy: Sin(x-y) = sinxcosy - sinycosx therefore, if you have sin3xcos2x - cos3xsin2x, it can be simplified into the above equation.
