Answer :

LHS


= tan 720° - cos 270° - sin 150° cos 120°


= tan (90° × 8 + 0°) – cos (90° × 3 + 0°) – sin (90° × 1 + 60°) cos (90° × 1 + 30°)


We know that when n is odd, cos sin and sin cos.


= tan 0° - sin 0° - cos 60° [-sin 30°]


= tan 0° - sin ° + cos 60° sin 30°


= 0 – 0 + 1/2 (1/2)


= 1/4


= RHS


Hence proved.


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