Solution: (1)
f(x)=sinx( 1-2sin？ θ/2) +cosxsinθ
=sinxcosθ +cosxsinθ
=sin(x+θ)
From 0
So there is f(π)=sin(π+θ) =-sinθ=- 1.
That is, sinθ= 1
So θ =π/2
The second question will also give you the answer:
F (x) = sin (x+θ) (0
f(A)=sin(A+θ)=√3/2
∴A+θ=π/3 or 2π/3
And θ =π/2 is obtained from (1).
∴A+θ=2π/3
∴A=2π/3 -π/2=π/6
According to the sine theorem, draw a conclusion
sinA=b/sinB
1/(sinπ/6)= ì3/sinB
sinB=√3/2
∴∠B=π/3
∴∠C=π-A-B=π/2