Question

36^sinx+36^cos(x+п/2)=37/6

Answer 1

$36^{sinx}+36^{cos(x+ frac{pi}{2} )}= frac{37}{6} \36^{sinx}+36^{-sinx}=frac{37}{6} \36^{sinx}=y, y in (0;+infty) \y+ frac{1}{y} =frac{37}{6} \y^2-frac{37}{6} *y+1=0 \6y^2-37y+6=0 \D=1369-144=1225=35^2 \y_1= frac{37+35}{12} =6 \y_2= frac{37-35}{12} = frac{1}{6} =6^{-1} \36^{sinx}=6 \6^{2sinx}=6^1 \2sinx=1 \sinx= frac{1}{2} \x_1= frac{pi}{6} +2pi n, n in Z \x_2= frac{5pi}{6} +2pi n, n in Z \36^{sinx}=6^{-1} \6^{2sinx}=6^{-1} \2sinx=-1$
$sinx=- frac{1}{2} \x_3= -frac{pi}{6} +2pi n, n in Z \x_4= -frac{5pi}{6} +2pi n, n in Z$