1.

Prove that: `sqrt((1-sinA)/(1+sinA))={(secA-tanA,if -pi/2 lt A lt pi/2),(tanA-secA ,if pi/2 lt A lt (3pi)/2):}`

Answer» LHS`=sqrt((1-sinA)/(1+sinA))=sqrt((1-sinA,1-sinA)/(1+sinA)), (1-sinA)(1-sinA)`
`=sqrt((1-sinA)^(2)/(1-sin^(2)A))= sqrt((1-sinA)^(2)/(cos^(2)A))=(1-sinA)/(|cosA|)`
`{{:((1-sinA)/(cosA)"," if -pi/2 lt "A" lt pi/2),((1-sinA)/(-cosA)"," if pi/2 lt Alt (3pi)/2):}`
`{{:(1/(cosA)-(sinA)/(cosA),if-pi/2ltAltpi/2),(-1/(cosA)+(sinA)/(cosA),if pi/2ltAlt(3pi)/2):}`
`{{:(secA-tanA,if-pi/2ltAltpi/2),(-secA+tanA,ifpi/2ltAlt(3pi)/2):}`
=RHS


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