Question

Show that 4(sin4 30o + cos4 60o ) – 3 (cos2 45o – sin2 90o ) = 2

Answer 1

4(sin4 30° + cos2 60°) − 3(cos2 45° − sin2 90°) − sin2 60° .....(i)

By trigonometric ratios we have

sin30∘=12 cos60∘=12 cos45∘=12 sin90∘=1 sin60∘=32

By substituting above values in (i), we get