Упростите выражение. [tex]1+sin(\frac{\pi}{2}-\alpha)cos(\pi-\alpha)-sin^2\alpha[/tex]. Created by hewwo. algebra-ru

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hewwo @hewwo

July 2022 1 14 Report

Упростите выражение.
[tex]1+sin(\frac{\pi}{2}-\alpha)cos(\pi-\alpha)-sin^2\alpha[/tex]

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juliaivanovafeo

Ответ:

Объяснение:

Используем формулы приведения и основное тригонометрическое тождество:

$1+sin(\frac{\pi}{2}-\alpha)cos(\pi-\alpha)-sin^2\alpha = \\\\ = 1+cos\alpha*(-cos(\alpha))-sin^2\alpha = \\\\= 1 - cos^{2}\alpha - sin^2\alpha = \\\\= 1 - (cos^{2}\alpha + sin^2\alpha) = 1 - 1 = 0$

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