Question

If coseca=2 then ( cota +sina/1+cosa)=2

Answer 1

Answer:

heres ur answer

Step-by-step explanation:

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.