Is 2cos^2(x)=cos(2x) ?

The answer to whether 2cos^2(x)=cos(2x) is False

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prove 2cos^2(x)=cos(2x)

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 0

2 cos^{2} (0) = 2

2 cos^{2} (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= 2 \cdot 1^{2}

Simplify

= 2

cos (2 \cdot 0) = 1

cos (2 \cdot 0)

Simplify

= cos (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= 1

The two sides are not equal

\Rightarrow False

tan (θ) cos (θ) - sin^{2} (θ) = cos^{2} (θ)

\frac{cot ^{2} ( θ )}{cos ^{2} ( θ )} = csc^{2} (θ)

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

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

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