Question

For the function f(x)=sinx, show with the formula sin^2A=1/2(1-cos2A) that f(x+y)-f(x)=cosxsiny-2sinxsin^2(1/2y)

Answer 1

f(x+y)-f(x) = sinx cosy + cosx siny - sinx

sin^2(1/2 y) = 1 - cosy

That should get you on your way... The rest is just algebra.

Answer 2

oops.

2sin^2(1/2 y) = 1 - cosy

Answer 3

I didn't get it

Answer 4

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