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Simplify the following without using tables.
Note: #root#𝑎#times##root#𝑎 = a
(a) sin 30° cos 30°
(b) 4 cos 45° sin 60°
(c) 3 cos 30° + cos 60°
(d) tan 45° + cos 45° sin 45°
(e) sin 60° cos 30° + Sin 30° cos 60°
(f) #cos^2#60°+#sin^2#60° (sin #theta# #times# sin #theta# is written as #sin^2##theta#)