Question

упростите выражение (cos2t/cost+sint) -cost; tg(-t)*cost-sin(4П-t)

Answer 1

$\boldsymbol{\dfrac{\cos(2t)}{\cos t + \cos t}-\cos t=}\dfrac{\cos^2t-\sin^2t}{\cos t + \cos t}-\cos t=\\\\=\dfrac{(\cos t-\sin t)(\cos t+\sin t)}{\cos t + \cos t}-\cos t=\\\\=\cos t-\sin t-\cos t\boldsymbol{=-\sin t}$

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$\boldsymbol{tg(-t)\cdot \cos t-\sin (4\pi - t)=}\\\\=-\dfrac{\sin t}{\cos t}\cdot \cos t+\sin t=-\sin t+\sin t\boldsymbol{=0}$

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Использованы формулы

cos (2α) = cos²α - sin²α

a² - b² = (a - b)(a + b)

tg (-α) = -tg α

sin (2π - α) = -sin α