Abstract
This chapter discusses fundamental trigonometric identities. The fundamental identities can be employed to prove or, more properly, to verify various trigonometric identities. There are also times in calculus and applied mathematics when simplification of a trigonometric expression may enable one to see a relationship which would otherwise be obscured. In computer applications, it is much more efficient to evaluate a simple trigonometric expression than an involved one. The preferred method of verifying an identity is to transform one side of the equation into the other. There are many trigonometric identities that are indeed of importance; these identities are called trigonometric formulas. The chapter discusses formulas in a logical sequence. It also discusses trigonometric equations that are not true for all values of the variable but may be true for some values. It has been shown that algebraic equations may have just one or two solutions. The situation is quite different with trigonometric equations as the periodic nature of the trigonometric functions assures that if there is a solution, then there are an infinite number of solutions.
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