Упростите выражение : 1 + (sin^4 a + sin^2 a * cos^2 a ) : cos^2 a. Created by Lapusha. algebra-ru

(учли основное тригонометрическое соотношение ) ответ:

Упростите выражение : 1 + (sin^4 a + sin^2 a * cos^2 a ) : cos^2 a...

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Упростите выражение : 1 + (sin^4 a + sin^2 a * cos^2 a ) : cos^2 a

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$1 +\frac {sin^{4} a + sin^{2} a * cos^{2} a}{cos^{2} a}= 1 +\frac {sin^{2} a(sin^{2} a+ cos^{2} a)}{cos^{2} a}=1+\frac {sin^2 {a}*1}{cos^{2} a}= 1+\frac {sin^2 {a}}{cos^{2} a}=\frac {cos^{2} a+sin^{2}a}{cos^{2} a}=\frac {1}{cos^{2}a}$

(учли основное тригонометрическое соотношение $cos^{2} a+sin^{2}a=1$ )

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