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! \(\displaystyle \text{How do I simplify the given }\sout{equation}\text{ expression ?}\) \(\displaystyle \;\;\;\sin3x\cdot\cos2x\,-\,cos3x\cdot\sin2x\) Click to expand... The quickest way is to recognize the compound-angle formula: \(\displaystyle \;\;\sin(A\,-\,B)\;=\;\sin(A)\cdot\cos(B)\,-\,\cos(A)\cdot\sin(B)\) We are given the right side of the formula with: \(\displaystyle \,A\,=\,3x,\;B\,=\,2x\) Answer: \(\displaystyle \,\sin(A\,-\,B)\;=\;\sin(3x\,-\,2x)\;=\;\sin x\)
Hello, zee! \(\displaystyle \text{How do I simplify the given }\sout{equation}\text{ expression ?}\) \(\displaystyle \;\;\;\sin3x\cdot\cos2x\,-\,cos3x\cdot\sin2x\) Click to expand... The quickest way is to recognize the compound-angle formula: \(\displaystyle \;\;\sin(A\,-\,B)\;=\;\sin(A)\cdot\cos(B)\,-\,\cos(A)\cdot\sin(B)\) We are given the right side of the formula with: \(\displaystyle \,A\,=\,3x,\;B\,=\,2x\) Answer: \(\displaystyle \,\sin(A\,-\,B)\;=\;\sin(3x\,-\,2x)\;=\;\sin x\)
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.
