Question

Prove:: sin 80° cos 20° - cos 80° sin 20° =√3/2​

Answer 1

Answer:

Given;

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

✔we know that,

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

$\sin(80 - 20) = sin80 \: cos20 - cos80 \: sin20$

According to the question,

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

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

Hence proved...

Thanks ❤

#kanika...

Answer 2

Using the formula

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

So,

$\sin(80) \cos(20) - \cos(80) \sin(20) \\ = > \sin(80 - 20) \\ = > \sin(60) \\ = > \frac{ \sqrt{3} }{2} = rhs \:$

Hence proved.