Nice try with the copy/paste. No workee here.
So just use your usual formulas.
f(x+y) = sin(x+y) = sinx cosy + cosx siny
so
f(x+y)-f(x) = sinx cosy + cosx siny - sinx
= sinx (cosy - 1) + cosx siny
= cosx siny - sinx (1 - cosy)
So now apply the double angle formula as given, and it all drops out
4. For the function 𝑓(𝑥) = 𝑠𝑖𝑛 𝑥 and using 𝑠𝑖𝑛2𝐴 =
1
2 (1 − cos 2𝐴). Show that
𝑓(𝑥 + 𝑦) − 𝑓(𝑥) = 𝑐𝑜𝑠 𝑥 𝑠𝑖𝑛 𝑦 – 2 𝑠𝑖𝑛 𝑥 𝑠𝑖𝑛2 (𝑦
2) ; 𝐴 =
𝑦
2
1 answer