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

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

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prove 3cos^2(x)-2=1-3sin^2(x)

prove

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

True

Solution steps

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

Manipulating left side

3 cos^{2} (x) - 2

Rewrite using trig identities

3 cos^{2} (x) - 2

Use the Pythagorean identity:

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

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

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

Simplify

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

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

Expand

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

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

Apply the distributive law:

a (b - c) = ab - a c

a = 3, b = 1, c = sin^{2} (x)

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

Multiply the numbers:

3 \cdot 1 = 3

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

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

Simplify

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

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

Group like terms

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

Add/Subtract the numbers:

3 - 2 = 1

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

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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sin^{2} (x) sec (x) csc (x) = tan (x)

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