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

p ro v e cos^{8} (x) = sin^{5} (x) cos^{3} (x)

p ro v e 2 sec (2 x) = tan (\frac{π}{4} + x) + tan (\frac{π}{4} - x)

p ro v e sin (x) - csc (x) = - (cos (x)) (cot (x))

p ro v e cos (θ) = sin (3 θ + 62)

p ro v e sin (π \cdot x) + sin (π \cdot (10 - x)) = 0

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