Question

 Chứng minh 
  a.  \((2sin^2x-1)tan^22x+3(2cos^2x-1)=0\)  
  b.  \(5sinx-2=3tan^2x(1-sinx)\) 

Answer 1

a) pt <=> - cos2x. tan²2x + 3.cos2x=0

      <=>  \(\dfrac{sin^22x}{-cos2x}\)+ 3cos2x =0

      <=>  sin²2x - 3cos²2x = 0

     <=> 1 - 4 cos²2x = 0

      <=> 1 - 4.\(\dfrac{1+cos4x}{2}\)= 0

      <=>  cos4x = \(\dfrac{-1}{2}\)