Question

Question #132a1

Answer 1

Please see below

Explanation:

`LHS=1-sin4x+cot((3pi)/4-2x)*cos4x`

`=1-sin4x+(cot((3pi)/4)*cot2x+1)/(cot2x-cot((3pi)/4))*cos4x`

`=1-sin4x+((cot(pi-pi/4)*cot2x+1)/(cot2x-cot(pi-pi/4)))*cos4x`

`=1-sin4x+(-cot(pi/4)*cot2x+1)/(cot2x-(-cot(pi/4)))*cos4x`

`=1-sin4x+(1-cot2x)/(1+cot2x)*cos4x`

`=1-sin4x+(1-(cos2x)/(sin2x))/(1+(cos2x)/(sin2x))*cos4x`

`=1-sin4x+(sin2x-cos2x)/(sin2x+cos2x)*cos4x`

`=1+(2(sin2x*cos4x-cos4x*cos2x-sin4x*sin2x-sin4x*cos2x))/(2(sin2x+cos2x))`

`=1+(sin(4x+2x)-sin(4x-2x)-cos(4x+2x)-cos(4x-2x)-cos(4x-2x)+cos(4x+2x)-sin(4x+2x)-sin(4x-2x))/(2(sin2x+cos2x)`

`=1+(sin6x-sin2x-cos6x-cos2x-cos2x+cos6x-sin6x-sin(2x))/(2(sin2x+cos2x)`

`=1-cancel((2(sin2x+cos2x))/(2(sin2x+cos2x)))`

`=1-1=0=RHS`