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(cos(80°)-cos(40°))/sin(40°) = ?

1 Answer

Oct 8, 2017

$\sqrt{3}$ $sqrt 3$

Explanation:

We know, cos C - cos D = - 2 sin(C + D)/2. sin (C - D)/2

Hence, $\frac{cos 80 - cos 40}{sin 40}$ $[ cos 80 - cos 40]/sin 40$

$\Rightarrow \frac{- 2 \frac{sin (80 + 40)}{2} . \frac{sin (80 - 40)}{2}}{sin 40}$ $rArr [ - 2 sin (80+40)/2. sin (80-40)/2]/sin 40$

$\Rightarrow \frac{- 2 sin 60 . sin 40}{sin 40}$ $rArr [ - 2 sin 60. sin 40]/sin 40$

$\Rightarrow - 2 sin 60$ $rArr - 2 sin 60$

$\Rightarrow - 2 . \frac{\sqrt{3}}{2} = - \sqrt{3}$ $rArr - 2. sqrt 3 /2 = - sqrt 3$

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