Question

prove that tan720-cos270-sin150cos120=1/4

Answer 1

tan 720=0
cos 270=0
-sin 150 cos120= -sin(180-150) cos(180-120)
=-sin 30 cos 60
= 1/4

Answer 2

Question:

tan 720°-cos 270°-sin150°×cos120° = 1/4

L.H.S.:

= tan 720°-cos 270°-sin150°×cos120°

= 0-0-sin (180°-30°)cos (180°-60°)

= (-sin180°×cos30°+cos180°sin30°) ×

(cos180°sin60°+sin180°sin60°)

= {-0×(√3/2)-1×(1/2)}×{-1×(1/2)+0×(√3/2)}

= (-1/2)×(-1/2)

= 1/4 = R.H.S. [Proved]