Answer:
1
Step-by-step explanation:
2cos²(80°)=1+cos(2(80°))
From trigonometry identity that states: cos2θ=2cos²θ-1
And from that we have: 2cos²θ=1+cos2θ
which makes 2cos²(80°)=1+cos(2(80°))
=1+cos(160°)
From the quadrant table, cosine is negative on the second quadrant i.e.
cos(180°-θ)=-cosθ
Therefore, cos(160°)=cos(180°-20°)=-cos(20°)
Going back to the original question,
cos(20°)+2cos²(80°)=cos(20°)+1+cos(160°)
=cos(20°)+1+(-cos(20°))
=cos(20°)+1-cos(20°)
=cos(20°)-cos(20°)+1
=1.
