Is 6cos^2(x)-3=3-6sin^2(x) ?

The answer to whether 6cos^2(x)-3=3-6sin^2(x) is True

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prove 6cos^2(x)-3=3-6sin^2(x)

prove

6 cos^{2} (x) - 3 = 3 - 6 sin^{2} (x)

True

Solution steps

6 cos^{2} (x) - 3 = 3 - 6 sin^{2} (x)

Manipulating left side

6 cos^{2} (x) - 3

Rewrite using trig identities

6 cos^{2} (x) - 3

Use the Pythagorean identity:

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

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

= 6 (1 - sin^{2} (x)) - 3

Simplify

6 (1 - sin^{2} (x)) - 3 : - 6 sin^{2} (x) + 3

6 (1 - sin^{2} (x)) - 3

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) - 3

Simplify

6 - 6 sin^{2} (x) - 3 : - 6 sin^{2} (x) + 3

6 - 6 sin^{2} (x) - 3

Group like terms

= - 6 sin^{2} (x) + 6 - 3

Add/Subtract the numbers:

6 - 3 = 3

= - 6 sin^{2} (x) + 3

= - 6 sin^{2} (x) + 3

= - 6 sin^{2} (x) + 3

= - 6 sin^{2} (x) + 3

= 3 - 6 sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

Is 6cos^2(x)-3=3-6sin^2(x) ?
The answer to whether 6cos^2(x)-3=3-6sin^2(x) is True