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

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

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

prove

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

True

Solution steps

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

Manipulating left side

(1 + cos (a)) (1 - cos (a))

Expand

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

= 1 - cos^{2} (a)

Use the Pythagorean identity:

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

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

= sin^{2} (a)

We showed that the two sides could take the same form

\Rightarrow True

csc (θ) - cos (θ) cot (θ) = sin (θ)

sin (x + \frac{π}{3}) + sin (x - \frac{π}{3}) = sin (x)

tan (u) (csc (u) - sin (u)) = cos (u)

sin (x - y) + sin (x + y) = 2 cos (y) sin (x)

(csc^{2} (x) - 1) sin (x) = cot^{2} (x) sin (x)

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