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61.
Base 10 logarithm
$\log_{10}x = \log x$
Logarithm
62.
Natural logarithm
$\log_e x = \ln x, e=2.718281...$
Logarithm
63.
Log to Ln
$\log x = \dfrac{\ln x}{\ln 10}$
Logarithm
64.
Ln to Log
$\ln x = \dfrac{\log x}{\log e}$
Logarithm
65.
$\sin\left(2\alpha\right)=2\sin\alpha \cos\alpha$
Double angle
Trigonometry
66.
$\cos\left(2\alpha\right)=\cos^2\alpha - \sin^2\alpha$
Double angle
Trigonometry
67.
$\tan\left(2\alpha\right)=\dfrac{2\tan\alpha}{1+\tan^2\alpha}$
Double angle
Trigonometry
68.
$\tan\left(2\alpha\right)=\dfrac{2}{\cot\alpha-\tan\alpha}$
Double angle
Trigonometry
69.
$\cot\left(2\alpha\right)=\dfrac{\cot^2\alpha-1}{2\cot\alpha}$
Double angle
Trigonometry
70.
$\cot\left(2\alpha\right)=\dfrac{\cot\alpha-\tan\alpha}{2}$
Double angle
Trigonometry
71.
Half Angle Formula of Sine
$\sin \dfrac{\alpha}{2} = \pm \sqrt{\dfrac{1-\cos\alpha}{2}}$
Half angle
Trigonometry
72.
Half Angle Formula of Cosine
$\cos \dfrac{\alpha}{2} = \pm \sqrt{\dfrac{1+\cos\alpha}{2}}$
Half angle
Trigonometry
73.
Half Angle Formula of Tangent
$\tan\dfrac{\alpha}{2} = \pm \sqrt{\dfrac{1-\cos\alpha}{1+\cos\alpha}}$
Half angle
Trigonometry
74.
Half Angle Formula of Tangent
$\tan \dfrac{\alpha}{2} = \dfrac{\sin\alpha}{1+\cos\alpha}$
Half angle
Trigonometry
75.
Half Angle Formula of Tangent
$\tan\dfrac{\alpha}{2} = \dfrac{1-\cos\alpha}{\sin\alpha}$
Trigonometry
Half angle
76.
Half Angle Formula of Cotangent
$\cot \dfrac{\alpha}{2} = \pm \sqrt{\dfrac{1+\cos\alpha}{1-\cos\alpha}}$
Half angle
Trigonometry
77.
Half Angle Formula of Cotangent
$\cot\dfrac{\alpha}{2} = \dfrac{\sin\alpha}{1-\cos\alpha}$
Half angle
Trigonometry
78.
Half Angle Formula of Cotangent
$\cot \dfrac{\alpha}{2} = \dfrac{1+\cos\alpha}{\sin\alpha}$
Half angle
Trigonometry
79.
$\sin\left(3\alpha\right)=3\sin\alpha-4\sin^3\alpha$
Trigonometry
80.
$\sin\left(3\alpha\right)=3\cos^2\alpha \cdot \sin \alpha-\sin^3\alpha$
Trigonometry

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