Question

Prove that : (i) `sin42^(@)cos48^(@)+sin48^(@)cos42^(@)=1`
(ii)`cos70^(@)cos20^(@)-sin70^(@)sin20^(@)=0`

Answer 1

(i) L.H.S. `=sin42^(@)cos48^(@)=sin48^(@)cos42^(@)`
`=sin42^(@)cos(90^(@)-42^(@))+sin(90^(@)-42^(@))cos42^(@)`
`=sin42^(@)sin42^(@)+cos42^(@)cos42^(@)`
`sin^(2)42^(@)+cos^(2)42^(@)`
`=1=R.H.S.`
(ii) L.H.S. `=cos70^(@)cos20^(@)-sin70^(@)sin20^(@)`
`=cos70^(@)cos20^(@)-sin(90^(@)-20^(@))sin(90^(@)-70^(@))`
`=cos70^(@)cos20^(@)-cos20^(@)-cos20^(@)cos70^(@)`
`=0=` R.H.S.