What is factor e^tsin(t)-e^{-t}sin(t) ?

The solution to factor e^tsin(t)-e^{-t}sin(t) is e^{-t}sin(t)(e^t+1)(e^t-1)

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factor e^tsin(t)-e^{-t}sin(t)

factor

e^{t} sin (t) - e^{- t} sin (t)

e^{- t} sin (t) (e^{t} + 1) (e^{t} - 1)

Solution steps

e^{t} sin (t) - e^{- t} sin (t)

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

e^{t} = e^{- t} e^{2 t}

= e^{- t} e^{2 t} sin (t) - e^{- t} sin (t)

Factor out common term

sin (t) e^{- t}

= sin (t) e^{- t} (e^{2 t} - 1)

Factor

e^{2 t} - 1 : (e^{t} + 1) (e^{t} - 1)

= e^{- t} sin (t) (e^{t} + 1) (e^{t} - 1)

(x + 7) + (x^{2})

x z - 5 x + 2 yz - 10 y

(1082)_{10}

x^{2} - 13 + 40

a^{2} + b c + ab + a c

What is factor e^tsin(t)-e^{-t}sin(t) ?
The solution to factor e^tsin(t)-e^{-t}sin(t) is e^{-t}sin(t)(e^t+1)(e^t-1)