# If A,B,C,D are thesmallest positive angles in ascending order of mag. which have their sines equal to the positive quantities K the values of 4sinA/2 +3sinB/2 +2sinC/2 +sin D/2?

Jitender Singh IIT Delhi
8 years ago
Ans: 5K
Sol:
A, B, C & D are vey small angles which means they all are very close to zero.
$sinA = sinB = sinC = sinD = K$
$sinA = 2.sin\frac{A}{2}.cos\frac{A}{2}$
$sin\frac{A}{2}=\frac{K}{2.cos\frac{A}{2}}$
Since A is very very close to zero, then
$cos\frac{A}{2} = 1$
$sin\frac{A}{2} = \frac{K}{2}$
Similarly for the other angles,
$sin\frac{A}{2}=sin\frac{B}{2}=sin\frac{C}{2}=sin\frac{D}{2} = \frac{K}{2}$
$4sin\frac{A}{2}+3sin\frac{B}{2}+2sin\frac{C}{2}+sin\frac{D}{2} = 4.\frac{K}{2}+3.\frac{K}{2}+2.\frac{K}{2}+\frac{K}{2}$
$=5K$
Thanks & Regards
Jitender Singh
IIT Delhi