Question

prove that

$sin80cos20 \: - \: cos80sin20 \: = \: (\sqrt{3} \div 2)$
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Answer 1

GIVEN :-

$\sf sin80cos20 - cos80sin20=\dfrac{\sqrt 3}{2}$

This is in the form :

• sinAcosB - cosAsinB

WE KNOW :-

$\huge\boxed{\bf sinAcosB-cosAsinB=sin(A-B)}$

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HERE :-

• A = 80

• B = 20

Applying the values to the equation ,

$\sf sin80cos20 - cos80sin20=sin(80-20)$

$\implies\sf sin80cos20 - cos80sin20=sin60$

We know ,

• $\sf sin60=\dfrac{\sqrt3}{2}$

Applying the value to the equation,

$\implies\sf sin80cos20 - cos80sin20=\dfrac{\sqrt 3}{2}$

$\huge\boxed{\bf HENCE\:PROVED\:\:!!!}$