Question

Решите уравнение cos(pi/2+t)-sin(pi-t)=1

Answer 1

$cos( dfrac{ pi }{2}+t)-sin( pi -t)=1 \ -sint-sint=1 \ sint=- dfrac{1}{2} \ left[begin{array}{I} x=- dfrac{pi}{6}+2 pi k \ x=- dfrac{5 pi }{6}+2 pi k end{array}}; k in Z$

Ответ: $left[begin{array}{I} x=- dfrac{pi}{6}+2 pi k \ x=- dfrac{5 pi }{6}+2 pi k end{array}}; k in Z$

Answer 2

$cos(frac{pi}{2}+t)-sin(pi-t)=1$

$-sin(t)-sin(t)=1$

$sin(t)=- frac{1}{2}$

$x = (-1)^{k+1}frac{pi}{6}+pi k, kin Z$