Use identity to simplify the expression? 2sin(π/9-π/2)cos(π/2-π/9)

1 Answer
Apr 2, 2018

2sin(pi/9-pi/2)cos(pi/2-pi/9)=-sin((2pi)/9)

Explanation:

We use sin(-A)=-sinA, sin(pi/2-A)=cosA, cos(pi/2-A)=sinA and 2sinAcosA=sin2A

sin(pi/9-pi/2)=sin(-(pi/2-pi/9))

= -sin(pi/2-pi/9)=-cos(pi/9)

Similarly cos(pi/2-pi/9)=sin(pi/9)

Hence 2sin(pi/9-pi/2)cos(pi/2-pi/9)

= -2cos(pi/9)*sin(pi/9)

= -2sin(pi/9)cos(pi/9)

= -sin((2pi)/9)