The given trigonometric function is sin 2 π 6 + cos 2 π 3 − tan 2 π 4 =− 1 2 .
Solve the left hand side of the trigonometric function.
L.H.S.= sin 2 π 6 + cos 2 π 3 − tan 2 π 4 = ( 1 2 ) 2 + ( 1 2 ) 2 − ( 1 ) 2 = 1 4 + 1 4 −1 =− 1 2
This is equal to the right hand side of the given trigonometric expression.
Thus, the trigonometric function is sin 2 π 6 + cos 2 π 3 − tan 2 π 4 =− 1 2 .
Since L.H.S. = R.H.S.
Hence proved.