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1) [tex] log_{ \sqrt{6} } ctgx=1+log _{6}( \frac{3}{2}-cos2x) [/tex]
2) [tex] log_{ 27 } (sin2x- \frac{1}{3}cosx) = \frac{1}{3} +log _{3}( -cosx) [/tex]
1) [tex] log_{ \sqrt{6} } ctgx=1+log _{6}( \frac{3}{2}-cos2x) [/tex]
2) [tex] log_{ 27 } (sin2x- \frac{1}{3}cosx) = \frac{1}{3} +log _{3}( -cosx) [/tex]
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Log₆¹/²(ctgx)=1+log₆(3/2-cos(2x))log₆(ctg²x)=log₆6+log₆(1,5-cos²x+sin²x)
log₆(ctg²x)=log₆(9-6cos²x+6sin²x)
ctg²x=(9sin²x+9cos²x)-6cos²x+6sin²x
cos²x/sin²x=15sin²x+3cos²x
cos²x/sin²x=15sin²x+3-3sin²x
cos²x/sin²x=12sin²x+3
cos²x=12sin⁴x+3sin²x
1-sin²x=12sin⁴x+3sin²x
12sin⁴x+4sin²x-1=0
sin²x=t>0
12t²+4t-1=0 D=64
t₁=1/6 t₂=-1/2 t₂∉
sin²x=1/6
sinx=√1/6 x₁=arcsin(√6/6)+2πn
sinx=-√√1/6 x₂=-arcsin(-√6/6)+2πn. x₂∉