1, solution: because S= 1/2(a*b)*sinc, sinc= 1/2, angle C = 30. Because BSINC = 1 = H. Push, (1/2*a)? +h？ =c？ ，c=2 .

2. Solution: 1/4*c? *tanA= 1/4*a？ Tambu, get an A? /c？ =

TanA/tanB, so b=c is an isosceles triangle, and a=b=c is an equilateral triangle.

3. Solution: By

Two angles sum formula sin(A+B)

=

sinAcosB+cosAsinB

And the angle doubling formula Sin2A=2SinA*CosA.

cos2a = COSA 2-Sina 2 = 1-2 Sina 2 = 2 COSA 2- 1。

F(x) = sin (2x+30) = sin {2 (x+15)}, so the period of f (x) is π.

When x+ 15 = π/4+nπ, y takes the maximum value, so the value range of x is π/6+nπ.

You work hard and everyone is happy. I hope it helps you.