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Question Number 75208 by vishalbhardwaj last updated on 08/Dec/19

 Prove that : cos 18^0 −sin 18^0  = (√2) sin 2

$$\:\mathrm{Prove}\:\mathrm{that}\::\:\mathrm{cos}\:\mathrm{18}^{\mathrm{0}} −\mathrm{sin}\:\mathrm{18}^{\mathrm{0}} \:=\:\sqrt{\mathrm{2}}\:\mathrm{sin}\:\mathrm{2} \\ $$

Answered by Kunal12588 last updated on 08/Dec/19

cos 18°−sin18°  =(√2)sin(45°−18°)  =(√2)sin(27°)≠(√2)sin 2

$${cos}\:\mathrm{18}°−{sin}\mathrm{18}° \\ $$$$=\sqrt{\mathrm{2}}{sin}\left(\mathrm{45}°−\mathrm{18}°\right) \\ $$$$=\sqrt{\mathrm{2}}{sin}\left(\mathrm{27}°\right)\neq\sqrt{\mathrm{2}}{sin}\:\mathrm{2} \\ $$

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