write the given sum as a product. You may need to use an Even/Odd or Cofunction Identity. sin(2θ) − sin(7θ)

Question

i have the answer it is -2Cos(9/2θ) Sin(5/2θ) i just dont know how to show my work any help would be awsome. thx alot

Answer 1

Mathew,

for ever, if f(c,d)=sin(c)-sin(d), then that is same as f(c,d)=2*cos((c+d)/2))*sin(c-d)/2))

look at [sin(a+b)]-[sin(a-b)]=[sin(a)*cos(b)+cos(a)*sin(b)]-[sin(a)*cos(b)-cos(a)*sin(b)]=2*cos(a)*sin(b)

sin(a+b)-sin(a-b) is the same as 2*cos(a)*sin(b)

when we see f(c,d)=sin(c)- sin(d)

we substitute, c=a+b, and d=a-b

adding these two conditions

a=(c+d)/2

and subtracting the conditions

b=(c-d)/2

so for ever sin(c)-sin(d)=2*cos((c+d)/2)*sin((c-d)/2)