Is (1+sin(α))(1-sin(α))=cos^2(α) ?

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

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prove (1+sin(α))(1-sin(α))=cos^2(α)

prove

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

True

Solution steps

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

Manipulating left side

(1 + sin (α)) (1 - sin (α))

Expand

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

= 1 - sin^{2} (α)

Use the Pythagorean identity:

1 = cos^{2} (α) + sin^{2} (α)

1 - sin^{2} (α) = cos^{2} (α)

= cos^{2} (α)

We showed that the two sides could take the same form

\Rightarrow True

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

1 + sin (x) = \frac{csc ( x ) + 1}{csc ( x )}

1 + sin (θ) = csc (θ)

\frac{1 + sin ( x )}{1 - sin ( x )} - \frac{1 - sin ( x )}{1 + sin ( x )} = \frac{4 tan ( x )}{cos ( x )}

sin (3 x) = 4 sin (x) \cdot cos^{2} (x) - sin (x)

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