if sinx+sin2x=2then find,cos2x+cos4x

Hi Vishwa Sharma

sinx+sin²x=2

=>sinx+sin²x-2=0

=>(sinx-1)(sinx+2)=0

=>sinx=1 or sinx=-2

 We know that sinx cannot be equal to -2.Hence rejaecting sinx=-2

 Therefore, sinx=1 =>x=pi/2

  cos²x+cos⁴x=xos²pi/2 + cos⁴pi/2 =0

sinx+sin²x=2

=>sinx=1+1-sin²x

=>sinx=1+cos²x

=>cos²x=sinx-1

now,

cos²x+cos⁴x

=cos²x+(sinx-1)²

=cos²x+sin²x-2sinx+1

=1-2sinx+1

=2(1-sinx)