In the text we showed that cos 2t = 1 2 sin2 t for 0 < t < /2 and substitution for t
Chapter 9, Problem 9.1.58(choose chapter or problem)
In the text we showed that cos 2t = 1 2 sin2 t for 0 < t < /2 and substitution for t shows that it is also true for t = 0 and t = /2. In this problem assume that /2 < t . (a) Show that cos 2( t)=1 2 sin2( t). (b) Use the periodicity and the evenness of the cosine function to show that cos 2( t) = cos 2t. (c) Use the fact that sin(t + ) = sin t to show that 1 2 sin2( t)=1 2 sin2 t. (d) Show that cos 2t = 1 2 sin2 t
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