Question

prove that sin80°cos20°-cos80°sin20°=√3/2​

Answer 1

Answer:

Given;

\sin(80) \cos(20) - \cos(80) \sin(20)sin(80)cos(20)−cos(80)sin(20)

✔we know that,

\sin(a - b) = \sin(a) \cos(b) - \cos(a) sin(b)sin(a−b)=sin(a)cos(b)−cos(a)sin(b)

\sin(80 - 20) = sin80 \: cos20 - cos80 \: sin20sin(80−20)=sin80cos20−cos80sin20

According to the question,

sin(80 - 20) = \frac{ \sqrt{3} }{2}sin(80−20)=

2

3

sin60 = \frac{ \sqrt{3} }{2}sin60=

2

3

Hence