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

EunoR

EunoR

Answered question

2021-05-02

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

Answer & Explanation

SchulzD

SchulzD

Skilled2021-05-03Added 83 answers

Substitute the given function: f(x+h)f(x)h=sin(x+h)sinxh
Use the the sine of a sum identity: sin(A+B)=sinAcosB+cosAsinB
f(x+h)f(x)h=sinxcosh+cosxsinhsinxh
Regroup as: f(x+h)f(x)h=sinxcoshsinx+cosxsinhh
Separate as: f(x+h)f(x)h=(sinxcoshsinxh)+(cosxsinhh)
Factor out sinxsinx from the first term and cosxcosx from the second term:
f(x+h)f(x)h=sinx(cosh1h)+cosx(sinhh)

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