Fill dotted lines. Show that |sin(x) − cos(x)| ≤ sqrt(2) for all x. Let f (x) = sin(x) − cos(x) on [0, 2?], since f has period 2?. f '(x) =.......  and f '(x) = 0   ⇔   cos(x) = ..........⇔ tan(x) = .....⇔ x = ......(entered as a comma-separated list). Evaluating f at its critical numbers and endpoints, we get  f (0) = ........ , f(3?/4) =........., f(7?/4) =.......... and f(2?) =..........  So f has absolute maximum value...........  and absolute minimum value ....... Thus,......≤ sin(x) − cos(x) ≤ ........ ⇒ |sin(x) − cos(x)| ≤.......

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.