Question

ПОМОГИТЕ С РЕШЕНИЕМ!

$frac{cos20 - cos140}{cos20 + cos140} =$

$frac{cos25 - cos85}{sin25 + sin85} =$
Это всё в градусах!

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Answer 1

$dfrac{cos20^circ-cos140^circ}{cos20^circ+cos140^circ}=dfrac{-2sinfrac{20^circ+140^circ}{2}sinfrac{20^circ-140^circ}{2} }{2cosfrac{20^circ+140^circ}{2}cosfrac{20^circ-140^circ}{2} }=-mathrm{tg}frac{20^circ+140^circ}{2}mathrm{tg}frac{20^circ-140^circ}{2}=\=-mathrm{tg}80^circmathrm{tg}(-60^circ)=mathrm{tg}80^circmathrm{tg}60^circ=mathrm{tg}80^circcdotsqrt{3} =sqrt{3}cdotmathrm{tg}80^circ$

$dfrac{cos25^circ-cos85^circ}{sin25^circ+sin85^circ}=dfrac{-2sinfrac{25^circ+85^circ}{2}sinfrac{25^circ-85^circ}{2} }{2sinfrac{25^circ+85^circ}{2}cosfrac{25^circ-85^circ}{2} }=-mathrm{tg}frac{25^circ-85^circ}{2}=\=-mathrm{tg}(-30^circ)=mathrm{tg}30^circ=dfrac{sqrt{3}}{3}$

Answer 2

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