Question

3tanA + cotA=5cosecA, find A if 0<=A<=90

Answer 1

3tanA+cotA=5cosecA
or, 3(sinA/cosA)+(cosA/sinA)=5/sinA
or, (3sin²A+cos²A)/cosAsinA=5/sinA
or, {3(1-cos²A)+cos²A}/cosA=5
or, 3-3cos²A+cos²A=5cosA
or, -2cos²A-5cosA+3=0
or, 2cos²A+5cosA-3=0
or, 2cos²A+6cosA-cosA-3=0
or, 2cosA(cosA+3)-1(cosA+3)=0
or, (2cosA-1)(cosA+3)=0
Either, 2cosA-1=0
or, 2cosA=1
or, cosA=1/2
Or, cosA+3=0
or, cosA=-3 which is not possible since -1≤cosФ≤1
∴, cosA=1/2
or, cosA=cos60°
or, A=60°