Question

\[\frac{\sin \theta}{1 + \cos \theta}\]is equal to 

Options

• \[\frac{\sin \theta}{1 + \cos \theta}\]

• \[\frac{1 - \cos \theta}{\cos \theta}\]

• \[\frac{1 - \cos \theta}{\cos \theta}\]

• \[\frac{1 - \sin \theta}{\cos \theta}\]

Answer 1

The given expression is `sin θ/(1+cosθ)`  

Multiplying both the numerator and denominator under the root by`(1-cosθ )` , we have 

`sinθ/(1+cos θ)`  

= `(sinθ (1-cos θ))/((1+cosθ)(1-cos θ))` 

=`(sin θ(1-cos θ))/(1-cos^2 θ)` 

= `(sin θ(1-cos θ))/sin^2 θ` 

= `(1-cos θ)/sin θ`