How do you express sin(pi/12) * cos(( pi)/2 ) without products of trigonometric functions?

1 Answer

color(blue)(sin (pi/12)*cos (pi/2)=1/2sin ((7pi)/12)-1/2sin ((5pi)/12))

Explanation:

Let us use the sum and difference formulas

sin (x+y)=sin x*cos y +cos x* sin y

sin (x-y)=sin x*cos y -cos x* sin y

After addition of equal values, we have

sin (x+y)+sin (x-y)=2*sin x*cos y

and we have the formula

sin x*cos y=1/2sin (x+y)+1/2sin (x-y)

We can now use the given

sin (pi/12)*cos (pi/2)=1/2sin (pi/12+pi/2)+1/2sin (pi/12-pi/2)

sin (pi/12)*cos (pi/2)=1/2sin ((7pi)/12)+1/2sin ((-5pi)/12)

sin (pi/12)*cos (pi/2)=1/2sin ((7pi)/12)-1/2sin ((5pi)/12)

God bless....I hope the explanation is useful.