if a,b,c,d are the smallest positive angles in ascending order of magnitude which have their sines equal to positive quantity - Physics - Basic Mathematics

Question

​if a,b,c,d are the smallest positive angles in ascending
order of magnitude which have their sines equal to positive
quantity k … then find value of 4sina/2 + 3sinb/2 + 2sinc/2
+ sind/2

Vaibhav T. · Accepted Answer

Dear Student,

According to question, a<b<c<dand sin a=sin b=sin c=sin d=kTherefore, 4 sina2+3 sinb2+2 sinc2+sind2=4 sina2+3 sinπ2-a2+2 sinπ+a2+sin3π2-a24 sina2+3 sinb2+2 sinc2+sind2=4 sina2+3 cosa2-2 sina2-cosa24 sina2+3 sinb2+2 sinc2+sind2=2 sina2+2 cosa24 sina2+3 sinb2+2 sinc2+sind2=2sina2+cosa24 sina2+3 sinb2+2 sinc2+sind2=21+sin a4 sina2+3 sinb2+2 sinc2+sind2=21+k

​if a,b,c,d are the smallest positive angles in ascending order of magnitude which have their sines equal to positive quantity k ….....then find value of 4sina/2 + 3sinb/2 + 2sinc/2 + sind/2

if a,b,c,d are the smallest positive angles in ascending order of magnitude which have their sines equal to positive quantity k ….....then find value of 4sina/2 + 3sinb/2 + 2sinc/2 + sind/2