What is sqrt(1+cos(x))*sqrt(1-cos(x)) ?

The solution to sqrt(1+cos(x))*sqrt(1-cos(x)) is sqrt((cos(x)+1)(-cos(x)+1))

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simplify sqrt(1+cos(x))*sqrt(1-cos(x))

simplify

1 + cos (x) \cdot 1 - cos (x)

(cos (x) + 1) (- cos (x) + 1)

Solution steps

1 + cos (x) 1 - cos (x)

Apply radical rule:

a b = a \cdot b,

assuming

a \geq 0, b \geq 0

cos (x) + 1 - cos (x) + 1 = (cos (x) + 1) (- cos (x) + 1)

= (cos (x) + 1) (- cos (x) + 1)

e^{- 2 t} cosh (t)

12 x (16 x^{4})

What is sqrt(1+cos(x))*sqrt(1-cos(x)) ?
The solution to sqrt(1+cos(x))*sqrt(1-cos(x)) is sqrt((cos(x)+1)(-cos(x)+1))