सिद्ध कीजिए कि
` sin ( - 420^(@) ) cos 390^(@) + cos ( -660^(@)) sin 330^(@) = -1 `

Explanation

` L.H.S = sin (-420^(@)) cos 390^(@)`
` + cos (- 660^(@))sin 330^(@)`
` = sin 420^(@) cos 390^(@) + cos 660^(@) sin 330^(@)`
` =- sin ( 360^(@) + 60^(@)) cos (360^(@) + 30^(@))`
` + cos ( 360^(@) + 300^(@)) sin ( 360^(@) -30^(@))`
` = - sin 60^(@) cos 30^(@) + cos 300^(@) ( - sin 30^(@))`
` = - (sqrt(3))/2 xx sqrt(3)/2 - 1/2 cos ( 360^(@) - 60^(@))`
` = -3/4 - 1/2 cos 60^(@) = -3/4 - 1/2 xx1/2 `
` = -3/4 -1/4 = -1 = R.H.S `