Is (1-cos(x))*(1-cos(x))=(1-cos(x))^2 ?

The answer to whether (1-cos(x))*(1-cos(x))=(1-cos(x))^2 is True

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prove (1-cos(x))*(1-cos(x))=(1-cos(x))^2

prove

(1 - cos (x)) \cdot (1 - cos (x)) = (1 - cos (x))^{2}

True

Solution steps

(1 - cos (x)) (1 - cos (x)) = (1 - cos (x))^{2}

Manipulating left side

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

Simplify

(1 - cos (x)) (1 - cos (x)) : (1 - cos (x))^{2}

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

Apply exponent rule:

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

(1 - cos (x)) (1 - cos (x)) = (1 - cos (x))^{1 + 1}

= (1 - cos (x))^{1 + 1}

Add the numbers:

1 + 1 = 2

= (1 - cos (x))^{2}

= (1 - cos (x))^{2}

= (1 - cos (x))^{2}

We showed that the two sides could take the same form

\Rightarrow True

Is (1-cos(x))*(1-cos(x))=(1-cos(x))^2 ?
The answer to whether (1-cos(x))*(1-cos(x))=(1-cos(x))^2 is True