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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Simplify

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

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

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) - 3 sin^{2} (x)

Add similar elements:

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

sec^{4} (x) = \frac{1}{cos ^{4} ( x )}

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

2 cos^{3} (x) - cos (x) = \frac{cos ^{2} ( x ) - sin ^{2} ( x )}{sec ( x )}

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