Correct Answer – a
`sin alpha sec (30^(@)+alpha)=1`
Shortcut method
Put `alpha` value between `0^(@)` to `60^(@)`
if `a=30^(@)`
`sin30^(@)sec(30^(@)+30^(@))=1`
`sin30^(@)sec60^(@)=1`
`(1)/(2)xx2=1`
1=1 (satisfy)
so `alpha=30^(@)`
`sin alpha+cos2alpha`
`=sin30^(@)+cos2xx30^(@)=sin30^(@)+cos60^(@)`
`=(1)/(2)+(1)/(2)=1`
Alternate
if `,sin alpha sec beta=1`
then `alpha+beta=90^(@)`
`sin alpha sec(30^(@)+alpha)=1`
`alpha+30^(@)+alpha=90^(@)`
`2alpha=60^(@)`
`alpha=30^(@)`
`sin alpha+cos2alpha`
`sin30+cos2xx30=1`