Question

Evaluate
2sin 40° cos 20°​

Answer 1

Answer:

$\sqrt{3}$

Step-by-step explanation:

Given  

2cos40-cos20÷sin20=has the value  

= cos 40 + (cos 40 – cos 20) / sin 20

= cos 40 – 2 sin (40 + 20/2) sin (40 – 20 / 2) / sin 20

= cos 40 – 2 sin 30 sin 10 / sin 20

= cos 40 – 2 x 1/2 sin 10 / sin 20

= cos 40 – sin 10 / sin 20

= cos (90 – 50 ) – sin 10 / sin 20

= sin 50 – sin 10 / sin 20

= 2 cos (50 + 10 / 2) sin (50 – 10 / 2) / sin 20

= 2 cos 30 sin 20 / sin 20

= 2 cos 30

= 2 x √3 / 2

= √3

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