Question

If tanθ= 1/2, then evaluate [(Cosθ/Sinθ) + {Sinθ/(1+Cosθ)}]​

Answer 1

Draw the triangle

you will find that as tanθ = perpendicular/base

perpendicular = x

base = 2x

which means hypotenuse = √5

To find=>[(1/tanθ)+{sinθ/(1+cosθ}]

=>[2+{(1/√5)/(1+2/√5)}]

=>2+ [(1/√5)*{(2√5-1)/(10-1)}] ---------------------- Factorizing the denominator

=>2+(2√5-1)/(9√5) -------- Answer(You can simplify more to your need