Basic IdentitiesClick here for the derivation of basic identities.
1. $\sin \theta = \dfrac{1}{\csc \theta}; \,\, \csc \theta = \dfrac{1}{\sin \theta}$ 2. $\cos \theta = \dfrac{1}{\sec \theta}; \,\, \sec \theta = \dfrac{1}{\cos \theta}$ 3. $\tan \theta = \dfrac{\sin \theta}{\cos \theta} = \dfrac{1}{\cot \theta}$ 4. $\cot \theta = \dfrac{\cos \theta}{\sin \theta} = \dfrac{1}{\tan \theta}$
In reference to the right triangle shown and from the functions of a right triangle: a/c = sin θ b/c = cos θ c/b = sec θ c/a = csc θ a/b = tan θ b/a = cot θ
The sum and difference of two angles can be derived from the figure shown below.
The Double Angle Formulas can be derived from Sum of Two Angles listed below: $\sin (A + B) = \sin A \, \cos B + \cos A \, \sin B$ → Equation (1)
$\cos (A + B) = \cos A \, \cos B - \sin A \, \sin B$ → Equation (2)
$\tan (A + B) = \dfrac{\tan A + \tan B}{1 - \tan A \, \tan B}$ → Equation (3)
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