Question #f4251

1 Answer
yumean1119
Dec 17, 2017

Use the formula #cos(90°-theta)=sintheta# and #sin2theta=2sinthetacostheta#.

Explanation:

Here is the proof:

#2cos70°cos20°#
#=2cos(90°-20°)cos20°#
#=2sin20°cos20°#
#=sin(2*20°)#
#=sin40°#
#=cos(90°-40°)#
#=cos50°#.

Or, there is another formula.
#2cosalphacosbeta=cos(alpha+beta)+cos(alpha-beta)#

Then,
#2cos70°cos20°#
#=cos(70°+20°)+cos(70°-20°)#
#=cos90°+cos50°#
#=cos50°#.

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