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

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

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

prove

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

True

Solution steps

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

Manipulating left side

(1 + sin (a)) (1 - sin (a))

Expand

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

(1 + sin (a)) (1 - sin (a))

Apply Difference of Two Squares Formula:

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

a = 1, b = sin (a)

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

Apply rule

1^{a} = 1

1^{2} = 1

= 1 - sin^{2} (a)

= 1 - sin^{2} (a)

Use the Pythagorean identity:

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

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

= cos^{2} (a)

We showed that the two sides could take the same form

\Rightarrow True

sin^{3} (θ) = \frac{3}{4} sin (θ) - \frac{1}{4} sin (3 θ)

tan^{2} (θ) + 1 = sec^{2} (θ)

sin (x) + sin (3 x) = 4 sin (x) cos^{2} (x)

\frac{cos ( x ) sec ( x )}{tan ( x )} = cot (x)

\frac{csc ^{2} ( t )}{cot ( t )} = csc (t) sec (t)

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