How do you express sin(π12)cos(π2) without products of trigonometric functions?

1 Answer

sin(π12)cos(π2)=12sin(7π12)12sin(5π12)

Explanation:

Let us use the sum and difference formulas

sin(x+y)=sinxcosy+cosxsiny

sin(xy)=sinxcosycosxsiny

After addition of equal values, we have

sin(x+y)+sin(xy)=2sinxcosy

and we have the formula

sinxcosy=12sin(x+y)+12sin(xy)

We can now use the given

sin(π12)cos(π2)=12sin(π12+π2)+12sin(π12π2)

sin(π12)cos(π2)=12sin(7π12)+12sin(5π12)

sin(π12)cos(π2)=12sin(7π12)12sin(5π12)

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