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

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

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

prove

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

True

Solution steps

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

Manipulating left side

3 cos^{2} (a) - 2

Rewrite using trig identities

3 cos^{2} (a) - 2

Use the Pythagorean identity:

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

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

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

Simplify

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

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

Expand

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

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

Apply the distributive law:

a (b - c) = ab - a c

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

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

Multiply the numbers:

3 \cdot 1 = 3

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

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

Simplify

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

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

Group like terms

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

Add/Subtract the numbers:

3 - 2 = 1

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

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

tan (A) = tan (A) csc^{2} (A) + cot (- A)

\frac{1}{1 + sin ( x )} = (sec (x) - tan (x)) sec (x)

(sec (x) + tan (x))^{2} = 1

tan (A) cot (A) = cos^{2} (A) + sin^{2} (A)

tan (a) + cot (a) = \frac{2}{sin ( 2 a )}

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