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

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

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

prove

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

True

Solution steps

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

Manipulating left side

(1 + sin (x)) (1 - sin (x))

Expand

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

(1 + sin (x)) (1 - sin (x))

Apply Difference of Two Squares Formula:

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

a = 1, b = sin (x)

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

Apply rule

1^{a} = 1

1^{2} = 1

= 1 - sin^{2} (x)

= 1 - sin^{2} (x)

Use the Pythagorean identity:

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

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

= cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (θ) + cos (θ) cot (θ) = csc (θ)

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

sin (x - \frac{π}{6}) + cos (x) = sin (x + \frac{π}{6})

sec (θ) sin (θ) = tan (θ)

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

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