MAT136H1 Lecture Notes - List Of Trigonometric Identities
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MAT136H1 Full Course Notes
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Reduction formula means a function that is raised to power of n can be recursively written in term of the function with lower power, and repeating the process, the integral can be eventually solved. To prove reduction formula, split the power into and , or even and depending on the function and its derivative (such as tangent, cotangent, cosecant, secant). Then apply integration by parts, simplify, and in the process there is a term which can be moved to the other side to be combined with the original integral. From there on through further simplifying process, the reduction formula is proven. Prove the reduction formula using integration by parts. Based on integration by parts, let and ( )( )( ) ( )( )( ) , and so and . Given the trigonometric identity ; , substitute into the integral: Move the middle term ( ) to the other side:
