Question

Применяя формулы двойных углов, решить задания

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Answer 1

Ответ:

$1)\ \ \dfrac{sin100^\circ }{sin50^\circ }=\dfrac{2\cdot sin50^\circ \cdot cos50^\circ }{sin50^\circ }=2\cdot cos50^\circ \\\\\\2)\ \ \dfrac{sin150^\circ }{cos75^\circ }=\dfrac{2\cdot sin75^\circ \cdot cos75^\circ }{cos75^\circ }=2\cdot sin75^\circ =2\cdot \dfrac{\sqrt6+\sqrt2}{4}=\dfrac{\sqrt6+\sqrt2}{2}$

$3)\ \ \dfrac{cos80^\circ }{cos40^\circ -sin40^\circ }=\dfrac{cos^240^\circ -sin^240^\circ }{cos40^\circ -sin40^\circ }=\dfrac{(cos40^\circ -sin40^\circ )(cos40^\circ +sin40^\circ )}{cos40^\circ -sin40^\circ }=\\\\=cos40^\circ +sin40^\circ$

$4)\ \ \dfrac{cos36^\circ +sin^218^\circ }{cos18^\circ }=\dfrac{cos^218^\circ -sin^218^\circ +sin^218^\circ }{cos18^\circ }=\dfrac{cos^218^\circ }{cos18^\circ }=\\\\=cos18^\circ=\dfrac{\sqrt{5+\sqrt5}}{2\sqrt2}=\dfrac{\sqrt{10+2\sqrt5}}{4}$