Is (6cos^2(x)-6sin^2(x))=6-12sin^2(x) ?

The answer to whether (6cos^2(x)-6sin^2(x))=6-12sin^2(x) is True

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prove (6cos^2(x)-6sin^2(x))=6-12sin^2(x)

prove

(6 cos^{2} (x) - 6 sin^{2} (x)) = 6 - 12 sin^{2} (x)

True

Solution steps

6 cos^{2} (x) - 6 sin^{2} (x) = 6 - 12 sin^{2} (x)

Manipulating left side

6 cos^{2} (x) - 6 sin^{2} (x)

Rewrite using trig identities

6 cos^{2} (x) - 6 sin^{2} (x)

Use the Pythagorean identity:

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

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

= 6 (1 - sin^{2} (x)) - 6 sin^{2} (x)

Simplify

6 (1 - sin^{2} (x)) - 6 sin^{2} (x) : 6 - 12 sin^{2} (x)

6 (1 - sin^{2} (x)) - 6 sin^{2} (x)

Expand

6 (1 - sin^{2} (x)) : 6 - 6 sin^{2} (x)

6 (1 - sin^{2} (x))

Apply the distributive law:

a (b - c) = ab - a c

a = 6, b = 1, c = sin^{2} (x)

= 6 \cdot 1 - 6 sin^{2} (x)

Multiply the numbers:

6 \cdot 1 = 6

= 6 - 6 sin^{2} (x)

= 6 - 6 sin^{2} (x) - 6 sin^{2} (x)

Add similar elements:

- 6 sin^{2} (x) - 6 sin^{2} (x) = - 12 sin^{2} (x)

= 6 - 12 sin^{2} (x)

= 6 - 12 sin^{2} (x)

= 6 - 12 sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

1 + \frac{1}{tan ^{2} ( x )} = csc^{2} (x)

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

sec (x \cdot 0) = 1

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

Is (6cos^2(x)-6sin^2(x))=6-12sin^2(x) ?
The answer to whether (6cos^2(x)-6sin^2(x))=6-12sin^2(x) is True