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

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

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

simplify

e^{c o s (x)} \cdot e^{- c o s (x)}

1

Solution steps

e^{c o s (x)} e^{- c o s (x)}

Apply exponent rule:

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

e^{c o s (x)} e^{- c o s (x)} = e^{c o s (x) - c o s (x)}

= e^{c o s (x) - c o s (x)}

Add similar elements:

cos (x) - cos (x) = 0

= e^{0}

Apply rule

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

= 1

1.81 \cdot 1 0^{- 5}

(1.5 \cdot 1 0^{0}) \cdot (2 \cdot 1 0^{- 5})

e^{- 4.8} (1 + 4.8 + \frac{4. 8 ^{2}}{2} + \frac{4. 8 ^{3}}{6})

e^{- \frac{7}{8}}