If cosA = cosB = -1/2 and A does not lie in the second quadrant and B does not lie - Maths - Trigonometric Functions

Question

If cosA = cosB = -1/2 and A does not lie in the second quadrant and
B does not lie in the third quadrant then find the value of 4Sin B
- 3 tanA/ tan B + Sin A

Vijay Kumar Gupta · Accepted Answer

It is given that,   cosA=cosB=-12Note that cosine function is negative only in second and third quadrant
So if A does not lie in 2nd quadrant, it must lie in 3rd quadrant
and if B does not lie in 3rd quadrant, it must lie in 2nd quadrant
 Now we have    cosA=-12  , Where A is in 3rd quadrant    cosA=-cosπ3       cosA=cosπ+π3      cosA=cos4π3           A=4π3Also, we have      cosB=-12  , Where B is in 2nd quadrant    cosB=-cosπ3       cosB=cosπ-π3      cosB=cos2π3           B=2π3So the value of sinA, sinB, tanA and tanB are,     sinA=sin4π3=sinπ+π3=-sinπ3=-32     sinB=sin2π3=sinπ-π3=sinπ3=32     tanA=sinAcosA=3     tanB=sinBcosB=-3Thus the value of given expression is,   4sinB-3tanAtanB+sinA=432-33-3-32                           =23-33-23-32                           =-3-332                           =23

If cosA = cosB = -1/2 and A does not lie in the second quadrant and B does not lie in the third quadrant then find the value of 4Sin B - 3 tanA/ tan B + Sin A.