`sec70^(@)sin20^(@)+cos20^(@)cosec70^(@)=2`
We have,sec 70° sin 20° +\xa0cos 20° cosec 70°= sec (90° – 20°) sin 20° +\xa0cos 20° cosec (90° – 20°)= cosec20° sin20° +\xa0cos20° sec20° [{tex}\\because{/tex}Sec(90°-A)=CosecA & Cosec(90° – A) = SecA ]{tex}= \\frac { \\sin 20 ^ { \\circ } } { \\sin 20 ^ { \\circ } } + \\frac { \\cos 20 ^ { \\circ } } { \\cos 20 ^ { \\circ } }{/tex}. [{tex}\\because{/tex}Cosec A=(1/SinA) & SecA =(1/CosA) ]= 1 +\xa01 = 2
`sec70^(@)sin(90^(@)-70^(@))+cos20^(@)cosec(90^(@)-20^(@))`
`=sec70^(@)cos70^(@)+cos20^(@)sec20^(@)`
`=(1)/(cos70^(@)).cos70^(@)+cos20^(@).(1)/(cos20^(@))`
=1+1=2.
Hence `sec70^(@)sin20^(@)+cos20^(@)cosec70^(@)=2`.