Is cos^2(x)= 1/2 (cos(2x)+1) ?

The answer to whether cos^2(x)= 1/2 (cos(2x)+1) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

prove cos^2(x)= 1/2 (cos(2x)+1)

prove

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

True

Solution steps

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

Manipulating right side

\frac{1}{2} (cos (2 x) + 1)

Rewrite using trig identities

\frac{1}{2} (cos (2 x) + 1)

Use the Double Angle identity:

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

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

Simplify

\frac{1}{2} (2 cos^{2} (x) - 1 + 1) : cos^{2} (x)

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

1 \cdot (2 cos^{2} (x) - 1 + 1) = 2 cos^{2} (x)

1 \cdot (2 cos^{2} (x) - 1 + 1)

- 1 + 1 = 0

= 1 \cdot 2 cos^{2} (x)

Multiply the numbers:

1 \cdot 2 = 2

= 2 cos^{2} (x)

= \frac{2 cos ^{2} ( x )}{2}

Divide the numbers:

\frac{2}{2} = 1

= cos^{2} (x)

= cos^{2} (x)

= cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

Is cos^2(x)= 1/2 (cos(2x)+1) ?
The answer to whether cos^2(x)= 1/2 (cos(2x)+1) is True