Trigonometry

[james_bond]

Prove that

[krtxmrtz]

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