1.

The set of all poddible ualuse of `alpha` in `[-pi,pi]` such that `sqrt((1-sinalpha)/(a+sinalpha))` is equal to sec `alpha-tanalpha,` isA. `[0,pi//2)`B. `[0,pi//2)uu(pi//2,pi)`C. `[-pi,0]`D. `(-pi//2,pi//2)

Answer» Correct Answer - C
Clearly, `sec alpha-tan alpha` is not difined for `alpha=+-pi//2.` Now,
`sqrt((1-sinalpha)/(1+sinalpha))=sqrt(((1-sinalpha)^(2))/(cos^(2)alpha))`
`impliessqrt((1-sinalpha)/(a+sinalpha))=(1-sinalpha)/(|cosalpha|)=sec alpha-tanalpha,if cos alphagt0`
Clearly, `cos alphagt0impliesalphain(-pi//2,pi//2)`


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