f.4 a.maths trigonmetric

1.in triangle abc let a/sinA=b/sinB=c/sinC=k

a) Show that a/sinA=a+b+c/sin a+sin b+sin c
b) Show that sinA+sinB+sinC=4cosA/2*cosB/2*cosC/2
c) Given that a+b+c=2m, by using the results of (a) and (b), show that a= m sin A/2secB/2secC/2

2.(a) By using the identity cos 2A=1-2sin^2A, show that
sin^2 x+sin^2 x+sin^2 3x = 3/2-1/2cos4x(2cos2x+1).
(b)find the general solution of the equation (sinx)^2+(sin2x)^2+(sin3x)^2=3/2