Is (1-cos(x))=cos(x)-1 ?

The answer to whether (1-cos(x))=cos(x)-1 is False

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prove (1-cos(x))=cos(x)-1

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

1 - cos (1) = 0.45969 \dots

1 - cos (1)

Refine to a decimal form

= 0.45969 \dots

cos (1) - 1 = - 0.45969 \dots

cos (1) - 1

Refine to a decimal form

= - 0.45969 \dots

The two sides are not equal

\Rightarrow False

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

sin (θ - \frac{π}{2}) + sin (θ + \frac{π}{2}) = 0

1 = cos^{2} (x) + sin^{2} (x)

(sin^{2} (x) + cos^{2} (x))^{3} = 1

tan^{2} (x) + 1 = \frac{1}{cot ^{2} ( x )} + 1