1.

If sec((pi)/(2)-alpha)+cosec((pi)/(2)-alpha).

Answer»

Solution :`sec((pi)/(2)-alpha)+COSEC((pi)/(2)-alpha)`
`=cosecalpha+secalpha=(1)/(SINALPHA)+(1)/(COSALPHA)=(cosalpha+sinalpha)/(sinalphacosalpha)`
`=(sinalpha+sinalpha)/(sinalphasinalpha)[:'sinalpha-cosalpha=0impliessinalphacosalpha]`
Again, `sinalpha=cosalpha=sin(90^(@)-alpha)`
`impliesalpha=90^(@)-alphaor,2alpha=90^(@)or,alpha=(90^(@))/(2)=45^(@)`
`:.(sinalpha+sinalpha)/(sinalpha.sinalpha)=(2sinalpha)/(sin^(2)alpha)=(2)/(sinalpha)=(2)/(sin45^(@))=(2)/((1)/(sqrt2))=2sqrt2`.
Hence `sec((pi)/(2)-alpha)+cosec((pi)/(2)-alpha)=2sqrt2`.


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