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Unformatted text preview: x = 12 sin 2 x = 2 cos 2 x1. Substituting x = π 8 gives: cos π 4 = 12 sin 2 π 8 ⇒ sin 2 π 8 = 1 2 1√ 2 2 ! ⇒ sin π 8 = r 1 2√ 2 4 (taking the positive square root, since π 8 is in quadrant 1). ∴ a = 1 2 and b =1 4 . Substituting x = π 8 gives: cos π 4 = 2 cos 2 π 81 ⇒ cos 2 π 8 = 1 2 √ 2 2 + 1 ! ⇒ cos π 8 = r √ 2 4 + 1 2 (taking the positive square root, since π 8 is in quadrant 1). ∴ c = 1 2 and d = 1 4 . 4. d dx cosh(sin x ) = d dx cosh( u ) where u = sin x = du dx ± d du cosh( u ) ² = cos x × sinh( u ) = cos x sinh(sin x ) ....
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 Three '11
 Continuous function, Inverse function, Injective function, positive square root

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