TRUE OR FALSE

Question

sin⁴x=(3/8)-(1/2) cos2x+(1/8)cos4x

Answer 1

sin² x =( 1-cos 2x)/2  so

 

LHS=( 1-cos2x)²/4=(1 + cos²2x -2cos 2x)/4

 

now cos²2x=( 1+ cos4x)/2

so LHS becomes  1/4+(1+cos4x)/8 -cos2x/2 which simplifies toRHS

Answer 2

(3/8)-(1/2)(1-2(sin(x)^2))+(1/8)(1-2(sin(2x)^2)

 

=(3/8)-(1/2)+(sin(x)^2)+(1/8)-(1/4)*4*(sin(x)^2)*(cos(x)^2)

 

=(3/8+1/8-1/2)+(sin(x)^2)(1-(cos(x)^2))

 

=(sin(x)^2)(1-(cos(x)^2))

 

=(sin(x)^4)

 

= left hand side