Prove that http://www.vbforums.com/attachment.p...1&d=1180353006
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cot(70) + 4cos(70) = sqr(3)
Multiply all by sin(70):
cos(70) + 4sin(70)cos(70) = sqr(3)sin(70) <--- This is what 'm going to prove
Formulas to be used:
sin(a - b) = sin(a)cos(b) - sin(b)cos(a)
sin(2a) = 2sin(a)cos(a)
sin(30) = 1/2
cos(30) = sqr(3)/2
Then:
cos(70) + 4sin(70)cos(70) = cos(70) + 2sin(140) = cos(70) + 2sin(180 - 40) = cos(70) + 2[sin(180)cos(40) - sin(40)cos(180)] = cos(70) + 2sin(40) = cos(70) + 2sin(70-30) = cos(70) + 2sin(70)cos(30) - 2sin(30)cos(70) = cos(70) + sqr(3)sin(70) - cos(70) = sqr(3)sin(70) QED