Question

\[\frac{x^2 - 1}{2x}\] is equal to 

Options

•  sec θ + tan θ

•  sec θ − tan θ

•  sec² θ + tan² θ

• sec² θ − tan² θ

Answer 1

The given expression is `sqrt ((1+sinθ)/(1-sinθ))`

Multiplying both the numerator and denominator under the root by `1+ sinθ`, we have 

`sqrt (((1+ sinθ)(1+sin θ))/((1+sin θ)(1-sinθ)))`     

`=sqrt((1+sinθ)/((1- sin^2θ)))` 

`= sqrt((1+ sinθ)^2/cos^2θ)`

=`(1+sinθ)/cosθ` 

=` 1/cosθ+sinθ/cosθ` 

=` sec θ+tan θ`