What is e^{sin(x)}*e^{-sin(x)} ?

The solution to e^{sin(x)}*e^{-sin(x)} is 1

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simplify e^{sin(x)}*e^{-sin(x)}

simplify

e^{s i n (x)} \cdot e^{- s i n (x)}

1

Solution steps

e^{s i n (x)} e^{- s i n (x)}

Apply exponent rule:

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

e^{s i n (x)} e^{- s i n (x)} = e^{s i n (x) - s i n (x)}

= e^{s i n (x) - s i n (x)}

Add similar elements:

sin (x) - sin (x) = 0

= e^{0}

Apply rule

a^{0} = 1, a \neq = 0

= 1

1.69 \cdot 1.44

3^{- 5} 0. 3^{2}

6 x^{2} y^{3} (x y)

(x - 1)^{2} (x + 1)^{2} (x^{2} + 1)^{2}

e^{- 0.0303}