Find the value of cosA : (1+cosA)/sinA = 1/2
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(1+cosA)/sinA=1/2
or, 2(1+cosA)=sinA
Squaring both sides,
4(1+cosA)²=sin²A
or, 4(1+2cosA+cos²A)=1-cos²A [∵, sin²A+cos²A=1]
or, 4+8cosA+4cos²A=1-cos²A
or, 5cos²A+8cosA+3=0
or, 5cos²A+5cosA+3cosA+3=0
or, 5cosA(cosA+1)+3(cosA+1)=0
or, (cosA+1)(5cosA+3)=0
Either, cosA+1=0
or, cosA=-1
Or, 5cosA+3=0
or, cosA=-3/5
∴, cosA=-1 or -3/5
or, 2(1+cosA)=sinA
Squaring both sides,
4(1+cosA)²=sin²A
or, 4(1+2cosA+cos²A)=1-cos²A [∵, sin²A+cos²A=1]
or, 4+8cosA+4cos²A=1-cos²A
or, 5cos²A+8cosA+3=0
or, 5cos²A+5cosA+3cosA+3=0
or, 5cosA(cosA+1)+3(cosA+1)=0
or, (cosA+1)(5cosA+3)=0
Either, cosA+1=0
or, cosA=-1
Or, 5cosA+3=0
or, cosA=-3/5
∴, cosA=-1 or -3/5
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