if cos theta = -1/2 and tan theta >0 show that 5tan theta + 4 sin theta/root 3 cos theta -3 sin theta is equal to 3

Dear student

 

theta = 240 degree hence sin theta = sqrt(3) /2

tan theta = sqrt(3)

 

hence 5 tan theta + 4 sin theta = 5 sqrt(3) - 2 sqrt(3) = 3 sqrt(3)

 

sqrt(3) cos theta – 3 sin theta = – sqrt3)/2 + 3 sqrt(3)/2 = sqrt(3)

 

hence now dividing = 3

 

Dear student 
CosQ = 1/2 
base = 1 
hypotaneous = 2 
perpendicular = rioot (3) 
tan Q = root(3)
sinQ = root(3)/2 
put in the equation 
LHS = [5root(3) + 2root(3)]/ [root(3)/2 - 3root(3)/2 ]
LHS = 3 
Which is equal to RHS