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{{ printedBook.courseTrack.name }} {{ printedBook.name }} The half-angle identities are special cases of angle difference identities. To evaluate trigonometric functions of half an angle, the following identities can be applied. The sign of each formula is determined by the quadrant in which $2θ $ lies.

$sin2θ cos2θ tan2θ =±21−cosθ =±21+cosθ =±1+cosθ1−cosθ $

First, write the Double-Angle Identity for the cosine.
$cos2x=2cos_{2}x−1 $
Next, solve this equation for $cosx.$
Finally, substitute $2θ $ for $x$ to obtain the required identity.

$cos2x=2cos_{2}x−1$

AddEqn$LHS+1=RHS+1$

$1+cos2x=2cos_{2}x$

Solve for $cosx$

DivEqn$LHS/2=RHS/2$

$21+cos2x =cos_{2}x$

RearrangeEqnRearrange equation

$cos_{2}x=21+cos2x $

SqrtEqn$LHS =RHS $

$cosx=±21+cos2x $

$cos2θ =±21+cos(2⋅2θ ) ⇓cos2θ =±21+cosθ $