Toán Lớp 11: Giải hộ em nha mng Sinx(2cos^3x+sinx+cosx)=1+2sin^2xcos^2x Giải chi tiết nha mng,em hứa vote 5 sao tất

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Toán Lớp 11:  Giải hộ em nha mng Sinx(2cos^3x+sinx+cosx)=1+2sin^2xcos^2x Giải chi tiết nha mng,em hứa vote 5 sao tất

annhocbichchaubich · Answer

$ begin{array}{l}  sin x left( {2{{ cos }^3}x +  sin x +  cos x}  right) = 1 + 2{ sin ^2}x{ cos ^2}x     Leftrightarrow 2 sin x{ cos ^3}x + { sin ^2}x +  sin x cos x = 1 + 2{ sin ^2}x{ cos ^2}x     Leftrightarrow 2 sin x{ cos ^3}x - 2{ sin ^2}x{ cos ^2}x + { sin ^2}x +  sin x cos x - 1 = 0     Leftrightarrow 2 sin x{ cos ^2}x left( { cos x -  sin x}  right) - { cos ^2}x +  sin x cos x = 0     Leftrightarrow 2 sin x{ cos ^2}x left( { cos x -  sin x}  right) +  cos x left( { sin x -  cos x}  right) = 0     Leftrightarrow  left( { sin x -  cos x}  right) left( { cos x - 2 sin x{{ cos }^2}x}  right) = 0     Leftrightarrow  cos x left( { sin x -  cos x}  right) left( {1 - 2 sin x cos x}  right) = 0     Leftrightarrow  cos x left( { sin x -  cos x}  right) left( {{{ sin }^2}x + {{ cos }^2}x - 2 sin x cos x}  right) = 0     Leftrightarrow  cos x left( { sin x -  cos x}  right){ left( { sin x -  cos x}  right)^2} = 0     Leftrightarrow  cos x{ left( { sin x -  cos x}  right)^3} = 0     Leftrightarrow  left[  begin{array}{l}  cos x = 0    sin x -  cos x = 0  end{array}  right.     Leftrightarrow  left[  begin{array}{l}  cos x = 0    sqrt 2  sin  left( {x -  dfrac{ pi }{4}}  right) = 0  end{array}  right.  Leftrightarrow  left[  begin{array}{l} x =  dfrac{ pi }{2} + k pi    x -  dfrac{ pi }{4} = k pi   end{array}  right.     Leftrightarrow  left[  begin{array}{l} x =  dfrac{ pi }{2} + k pi    x =  dfrac{ pi }{4} + k pi   end{array}  right. left( {k  in  mathbb{Z}}  right)  end{array}$