Ответ:
a) (tg^2x - 1) * sqrt(13cosx) = 0;
tg^2x - 1 = 0 или sqrt(13cosx) = 0;
tg^2x = 1
tgx = +-1
x = pi/4 + pin, n ∈ Z;
x = -pi/4 + pin, n ∈ Z;
sqrt(13cosx) = 0;
13cosx = 0;
cosx = 0;
x = pi/2 + pin, n ∈ Z;
б) -3pi <= pi/4 + pin <= -3pi/2;
-12pi/4 - pi/4 <= pin <= -6pi/4 - pi/4;
-13pi/4 <= pin <= -7pi/4;
n = -3, n = -2: x = pi/2 - 2pi = -3pi/2; x = pi/2 - 3pi = -5pi/2;
-3pi <= pi/2 + pin <= -3pi/2;
-3pi - pi/2 <= pin <= -3pi/2 - pi/2;
-7pi/2 <= pin <= -4pi/2;
-3,5 <= n <= -2;
n = -3, n = -2: x = pi/2 - 3pi = -5pi/2, x = pi/2 - 2pi = -3pi/2.
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Answers & Comments
Ответ:
a) (tg^2x - 1) * sqrt(13cosx) = 0;
tg^2x - 1 = 0 или sqrt(13cosx) = 0;
tg^2x = 1
tgx = +-1
x = pi/4 + pin, n ∈ Z;
x = -pi/4 + pin, n ∈ Z;
sqrt(13cosx) = 0;
13cosx = 0;
cosx = 0;
x = pi/2 + pin, n ∈ Z;
б) -3pi <= pi/4 + pin <= -3pi/2;
-12pi/4 - pi/4 <= pin <= -6pi/4 - pi/4;
-13pi/4 <= pin <= -7pi/4;
n = -3, n = -2: x = pi/2 - 2pi = -3pi/2; x = pi/2 - 3pi = -5pi/2;
-3pi <= pi/2 + pin <= -3pi/2;
-3pi - pi/2 <= pin <= -3pi/2 - pi/2;
-7pi/2 <= pin <= -4pi/2;
-3,5 <= n <= -2;
n = -3, n = -2: x = pi/2 - 3pi = -5pi/2, x = pi/2 - 2pi = -3pi/2.