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21.
Half Angle Formula of Cosine
$\cos \dfrac{\alpha}{2} = \pm \sqrt{\dfrac{1+\cos\alpha}{2}}$
22.
Half Angle Formula of Tangent
$\tan\dfrac{\alpha}{2} = \pm \sqrt{\dfrac{1-\cos\alpha}{1+\cos\alpha}}$
23.
Half Angle Formula of Tangent
$\tan \dfrac{\alpha}{2} = \dfrac{\sin\alpha}{1+\cos\alpha}$
24.
Half Angle Formula of Tangent
$\tan\dfrac{\alpha}{2} = \dfrac{1-\cos\alpha}{\sin\alpha}$
25.
Half Angle Formula of Cotangent
$\cot \dfrac{\alpha}{2} = \pm \sqrt{\dfrac{1+\cos\alpha}{1-\cos\alpha}}$
26.
Half Angle Formula of Cotangent
$\cot\dfrac{\alpha}{2} = \dfrac{\sin\alpha}{1-\cos\alpha}$
27.
Half Angle Formula of Cotangent
$\cot \dfrac{\alpha}{2} = \dfrac{1+\cos\alpha}{\sin\alpha}$
38.
Sum of sines
$\sin \alpha + \sin \beta = 2 \cdot \sin\dfrac{\alpha+\beta}{2}\cdot \cos \dfrac{\alpha-\beta}{2}$
39.
Difference of sines
$\sin \alpha - \sin \beta = 2\cdot \sin\dfrac{\alpha - \beta}{2} \cdot \cos \dfrac{\alpha+\beta}{2}$
40.
Sum of cosines
$\cos\alpha + \cos\beta = 2 \cdot \cos \dfrac{\alpha+\beta}{2} \cdot \cos \dfrac{\alpha-\beta}{2}$