Is (1-sin(3a))(sin(3a)+1)=cos^2(3a) ?

The answer to whether (1-sin(3a))(sin(3a)+1)=cos^2(3a) is True

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prove (1-sin(3a))(sin(3a)+1)=cos^2(3a)

prove

(1 - sin (3 a)) (sin (3 a) + 1) = cos^{2} (3 a)

True

Solution steps

(1 - sin (3 a)) (sin (3 a) + 1) = cos^{2} (3 a)

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

(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)

\Rightarrow True

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

cos^{2} (\frac{( 12 π )}{2}) = cos^{2} (12 π)

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

sec (t) (csc (t) (tan (t) + cot (t))) = sec^{2} (t) + csc^{2} (t)

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

Is (1-sin(3a))(sin(3a)+1)=cos^2(3a) ?
The answer to whether (1-sin(3a))(sin(3a)+1)=cos^2(3a) is True