Evaluate 1 + cos? /1-cos?

We need to evaluate 1+cosΘ /1-cosΘ

Solution

1+cosΘ /1-cosΘ

The given equation can be simplified using the identity (a-b) (a+b) = (a2-b2)

1+cosΘ /1-cosΘ= ( 1 – cos2Θ) ———–(i)

We know that sin2Θ + cos2Θ = 1 substituting 1= sin2Θ + cos2 Θin equation (i) we get,

[(sin2Θ + cos2Θ – cos2Θ]

Combining the like terms we get

=sin2Θ + (cos2 Θ – cos2 Θ)

=sin2 Θ

Answer

1+cosΘ /1-cosΘ= sin2 Θ

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