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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
Solution
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`
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