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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Rewrite using trig identities

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

Use the Double Angle identity:

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

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

Simplify

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

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

Multiply fractions:

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

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

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

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

Simplify

1 + 2 cos^{2} (B) - 1 : 2 cos^{2} (B)

1 + 2 cos^{2} (B) - 1

Group like terms

= 2 cos^{2} (B) + 1 - 1

1 - 1 = 0

= 2 cos^{2} (B)

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

Multiply the numbers:

1 \cdot 2 = 2

= 2 cos^{2} (B)

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

Divide the numbers:

\frac{2}{2} = 1

= cos^{2} (B)

= cos^{2} (B)

= cos^{2} (B)

We showed that the two sides could take the same form

\Rightarrow True

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

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