- #1
andrewkg
- 86
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Q.
Use the addition formula cos(u+v) = cos(u)cos(v) - sin(u)sin(v) to derive the following identity for the average rate of change of the cosine function:
(cos(x + h) - cos x) / h = cos x ((cos h - 1) / h) - sin x ((sin h) / h)
A.
cos(x+h) = cosxcosh - sinxsinh
subtitute this to (cos(x+h) - cos x)/h we get
(cos(x+h) - cos x)/h = (cosxcosh - sinxsinh -cosx)/h
then I know it must go down to =(cosx(cosh - 1) - sinxsinh)/h
but how does cosxcosh - cosx simpify to cosx(cosh-1)
?
sorry my really basic skills are poor
Thank you a ton!
Use the addition formula cos(u+v) = cos(u)cos(v) - sin(u)sin(v) to derive the following identity for the average rate of change of the cosine function:
(cos(x + h) - cos x) / h = cos x ((cos h - 1) / h) - sin x ((sin h) / h)
A.
cos(x+h) = cosxcosh - sinxsinh
subtitute this to (cos(x+h) - cos x)/h we get
(cos(x+h) - cos x)/h = (cosxcosh - sinxsinh -cosx)/h
then I know it must go down to =(cosx(cosh - 1) - sinxsinh)/h
but how does cosxcosh - cosx simpify to cosx(cosh-1)
?
sorry my really basic skills are poor
Thank you a ton!