Is (1+cos(x))(1-cos(x))=sin^2(x) ?

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

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prove (1+cos(x))(1-cos(x))=sin^2(x)

prove

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

True

Solution steps

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

Manipulating left side

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

Expand

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

= 1 - cos^{2} (x)

Use the Pythagorean identity:

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

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

= sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

(sec (x) + 1) (sec (x) - 1) = tan^{2} (x)

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

4 sin^{2} (θ) + 2 cos^{2} (θ) = 4 - 2 cos^{2} (θ)

sin^{2} (2 x) = 4 sin^{2} (x) cos^{2} (x)

(sec (x) - 1) (sec (x) + 1) = tan^{2} (x)

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