Indeterminate Forms in Trigonometry

The subject of indeterminate forms is usually treated in algebra or in calculus; and hence it seldom occurs to the student that these forms may occur in trigonometry. It is sometimes desirable to examine critically some of the operations in proving identities, so that a false conclusion may not be drawn. Frequently the process of dividing both numerator and denominator by a factor holds only for certain values of the variable, or variables, involved. The occasional presence of indeterminates in solving spherical triangles teaches us that a spherical triangle is not always determined when three parts are given, as is sometimes supposed.