If `(pi)/(2)lt thetalt(3pi)/(2),then sqrt((1-sintheta)/(1+sintheta))"is equal to"`

Options

A. `sec theta-tan theta`
B. `sec theta+tan theta`
C. `tha theta-sec theta`
D. none of these

Answer

C

Explanation

We have,
`sqrt((1-sintheta)/(1+sin theta))=sqrt(((1-sintheta)^(2))/(1-sin^(2)theta))`
`impliessqrt((1-sintheta)/(1+sintheta))=(1-sintheta)/(|costheta|)`
`impliessqrt((1-sin theta)/(1+sin theta))=(-1sintheta)/(-costheta)" "[because(pi)/(2)lt theta(3pi)/(2)impliescosthetalt0]`
`impliessqrt((1-sintheta)/(1+sintheta))=-sectheta+tan theta`