(sin(10°)+sin(20°)+sin(40°)+sin(50°))/(cos(10°)+cos(20°)+cos(40°)+cos(50°)) = ?

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(sin(10°)+sin(20°)+sin(40°)+sin(50°))/(cos(10°)+cos(20°)+cos(40°)+cos(50°)) = ?

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Answer 1 · 2017-10-09T02:48:10

$- 6.405331191$ $-6.405331191$

Explanation:

$\frac{sin (10) + sin (20) + sin (40) + sin (50)}{cos (10) + cos (20) + cos (40) + cos (50)}$ $(sin(10)+sin(20)+sin(40)+sin(50))/(cos(10)+cos(20)+cos(40)+cos(50))$
You need to punch in each term in a calculator, sum up the numerator and denominator separately, then divide the two sums.

Answer 2 · 2017-10-09T03:19:03

$\frac{sin (10) + sin (20) + sin (40) + sin (50)}{cos (10) + cos (20) + cos (40) + cos (50)}$ $(sin(10)+sin(20)+sin(40)+sin(50))/(cos(10)+cos(20)+cos(40)+cos(50))$

$= \frac{sin (10) + sin (50) + sin (40) + sin (20)}{cos (10) + cos (50) + cos (40) + cos (20)}$ $=(sin(10)+sin(50)+sin(40)+sin(20))/(cos(10)+cos(50)+cos(40)+cos(20))$

$= \frac{2 sin (30) cos (20) + 2 sin (30) cos (10)}{2 cos (30) cos (20) + 2 cos (30) cos (10)}$ $=(2sin(30)cos(20)+2sin(30)cos(10))/(2cos(30)cos(20)+2cos(30)cos(10))$

$= \frac{2 \cdot \frac{1}{2} \cdot cos (20) + 2 \cdot \frac{1}{2} \cdot cos (10)}{2 \cdot \frac{\sqrt{3}}{2} \cdot cos (20) + 2 \cdot \frac{\sqrt{3}}{2} \cdot cos (10)}$ $=(2*1/2*cos(20)+2*1/2*cos(10))/(2*sqrt3/2*cos(20)+2*sqrt3/2*cos(10))$

$= \frac{cos (20) + cos (10)}{\sqrt{3} (cos (20) + cos (10))} = \frac{1}{\sqrt{3}}$ $=(cos(20)+cos(10))/(sqrt3(cos(20)+cos(10)))=1/sqrt3$

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(sin(10°)+sin(20°)+sin(40°)+sin(50°))/(cos(10°)+cos(20°)+cos(40°)+cos(50°)) = ?

2 Answers

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