Question

Find cos(20°)+2cos^2 (80°)
help me pls.​

Answer 1

i did not understand your question

Explanation:

Answer 2

1

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.