Sin (60°+theta)-cos (30°-theta)=?

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Answer 1 · 2018-03-10T05:59:21

#0#

Given: #sin(60^o + theta) - cos(30^o-theta)#

Use the sum and difference formulas:
#sin(u+v) = sin u cos v + cos u sin v#
#cos(u-v) = cos u cos v + sin u sin v#

#sin 30^o = 1/2; " "cos 30^o = (sqrt(3))/2#

#sin 60^o = (sqrt(3))/2; " "cos 60^o = 1/2#

#sin(60^o + theta) = sin60^o cos theta + cos 60^o sin theta#
# = (sqrt(3))/2 cos theta + 1/2 sin theta#

#cos(30^o-theta) = cos 30^o cos theta + sin 30^o sin theta#
#= (sqrt(3))/2 cos theta + 1/2 sin theta#

#sin(60^o + theta) - cos(30^o-theta) =#

# (sqrt(3))/2 cos theta + 1/2 sin theta - (sqrt(3))/2 cos theta - 1/2 sin theta = 0#