help!

for the function f(x) = sinx, show with the aid of elementary formula Sin^2 A= ½ (1-cos2A) that:

f(X + Y) - f(X) = cosXsinY-2sinXsin ^{2} (\frac{ 1 }{ 2 }Y)

Question

help!

for the function f(x) = sinx, show with the aid of elementary formula Sin^2 A= ½ (1-cos2A) that: 

f(X + Y) - f(X) = cosXsinY-2sinXsin ^{2} (\frac{ 1 }{ 2 }Y)

anonymous · Answer

$$f(X + Y) - f(X) = cosXsinY-2sinXsin ^{2} (\frac{ 1 }{ 2 }Y)$$

here's a clearer equation for my question, please help me :(

mertsj · Answer

$$f(x+y)=\sin (x+y)=\sin x \cos y+\cos x \sin y$$

mertsj · Answer

$$f(x+y)-f(x)=\sin x \cos y+\cos x \sin y-\sin x=\cos x \sin y+\sin x(\cos y-1)$$

mertsj · Answer

But I don't know how to get sin^2

anonymous · Answer

im actually confused about the sin^2 thing too, and also i am confused how to get the 1/2

anonymous · Answer

Given the elementary formula you can work backwards. For instance say A = Y/2, then $$\sin^2(A) = 1/2(1 - \cos(y))$$, so $$-2\sin(x)\sin^2(Y/2) = -2\sin(x)[(1/2(1 - \cos(y))]$$ and after you simply that you will end up with sin(x)(-1 + cos(y))