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Main articles: Identity (mathematics) and List of trigonometric identities An identity is a statement resembling an equation which is true for all possible values of the variable(s) it contains. Many identities are known, especially in trigonometry. Probably the best known example is: \sin^2(\theta)+\cos^2(\theta)=1,, which is true for all values of θ. In the process of solving an equation, it is often useful to combine it with an identity to produce an equation which is more easily soluble. For example, to solve the equation: 3\sin(\theta) \cos(\theta)= 1, where θ is known to be between zero and 45 degrees, use the identity: \sin(2 \theta)=2\sin(\theta) \cos(\theta), so the above equation becomes: \frac{3}{2}\sin(2 \theta) = 1 Whence: \theta = \frac{1}{2} \arcsin\left(\frac{2}{3}\right) \approx 20.9^\circ. |
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