Given that f(x)=cosx, show that (f(x+h)-f(x))/h=cosx((cosh-1)/h)+sinx(sinh/h)

usagirl007A

usagirl007A

Answered question

2021-05-28

Given that f(x)=cosx, show that f(x+h)f(x)h=cosx(cosh1h)+sinx(sinhh)

Answer & Explanation

opsadnojD

opsadnojD

Skilled2021-05-29Added 95 answers

Substitute the given function: f(x+h)f(x)h=cos(x+h)cosxh
Use the the sine of a sum identity: sin(A+B)=sinAcosB+cosAsinB f(x+h)f(x)h=cosxcoshsinxsinhcosxh
Regroup as: f(x+h)f(x)h=cosxcoshcosxsinxsinhh
Separate as: f(x+h)f(x)h=(cosxcoshcosxh)(sinxsinhh)
Factor out sinxsinx from the first term and cosxcosx from the second term:
f(x+h)f(x)h=cosx(cosh1h)sinx(sinhh)
Jeffrey Jordon

Jeffrey Jordon

Expert2021-08-11Added 2605 answers

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