Is (1+cos(α))(1-cos(α))=sin^2(α) ?

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

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prove (1+cos(α))(1-cos(α))=sin^2(α)

prove

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

True

Solution steps

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

Manipulating left side

(1 + cos (α)) (1 - cos (α))

Expand

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

(1 + cos (α)) (1 - cos (α))

Apply Difference of Two Squares Formula:

(a + b) (a - b) = a^{2} - b^{2}

a = 1, b = cos (α)

= 1^{2} - cos^{2} (α)

Apply rule

1^{a} = 1

1^{2} = 1

= 1 - cos^{2} (α)

= 1 - cos^{2} (α)

Use the Pythagorean identity:

1 = cos^{2} (α) + sin^{2} (α)

1 - cos^{2} (α) = sin^{2} (α)

= sin^{2} (α)

We showed that the two sides could take the same form

\Rightarrow True

tan (\frac{π}{2} - θ) = cot (θ)

sin^{3} (x) cos^{2} (x) = sin^{3} (x) - sin^{5} (x)

\frac{cos ( x ) cot ( x )}{1 - sin ( x )} = csc (x)

sec (2 a) = \frac{csc ^{2} ( a )}{cot ^{2} ( a ) - 1}

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

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