Question

If cosecA = 2 , find the value of 1/tanA + sinA/1+cos A

Answer 1

cosecA=2
or, 1/sinA=2
or, sinA=1/2
∵, sin²A+cos²A=1
or, cos²A=1-sin²A
or, cos²A=1-1/4
or, cos²A=3/4
or, cosA=√3/2 (neglecting the negative sign)
∴, tanA=sinA/cosA=(1/2)/(√3/2)=1/√3
∴, 1/tanA+sinA/(1+cosA)
=1/(1/√3)+(1/2)/(1+√3/2)
=√3+(1/2)/{(2+√3)/2}
=√3+1/(2+√3)
={√3(2+√3)+1}/(2+√3)
=(2√3+3+1)/(2+√3)
=(4+2√3)/(2+√3)
=2(2+√3)/(2+√3)
=2 Ans.