Question

In a ΔABC , 3sinx -4 sin² x - k=0 , 0 Find the measure of

Answer 1

A , B , C are angle of triangle also this angle satisfied given equation.
now,
3sinA-4sin^3A-k=0 => sin3A=k

3sinB-4sin^3B-k=0 =>sin3B=k

3sinC-4sin^3C-k=0 => sin3C=k

here we see all
sin3A=sin3B=sin3C =k
sin3A=sin3B
sin3A=sin(180°-3B)
3A+3B=180°
A+B=60°----------(1)
but we know ,
sum of all angles of triangle is are 180°
e.g. A+B+C=180°
form equation (1)
60°+C=180°
C=120°
hence k=sin3C=sin360°=0
k=0