In the triangle ABC, ABC =90, AC=√2 and AB = BC +1. (a) Show that cos 4-sin  =- (b) By squaring both sides of the equation in part (a), solve the equation to find the angles in the triangle. (c) Apply Pythagoras' theorem in the triangle ABC to find BC, and hence show that √6-√2 sin = 4 (d) Hence, or otherwise, calculate the length of the perpendicular from B to [AC].

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