How do you simplify $\frac{1 - cos 100}{sin 100}$ $(1-cos100)/sin100$ ?

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How do you simplify $\frac{1 - cos 100}{sin 100}$ $(1-cos100)/sin100$ ?

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Answer 1 · 2016-06-27T14:43:34

tan (50)

Explanation:

Apply the 2 trig identities:
$1 - cos 2 a = 2 {sin}^{2} a$ $1 - cos 2a = 2sin^2 a$
$sin 2 a = 2 sin a . cos a$ $sin 2a = 2sin a.cos a$ ,
We get:
$1 - cos (100) = 2 {sin}^{2} (50)$ $1 - cos (100) = 2sin^2 (50)$
$sin (100) = 2 sin 50 . cos 50$ $sin (100) = 2sin 50.cos 50$
$y = \frac{1 - cos (100)}{sin (100)} = \frac{2 {sin}^{2} (50)}{2 sin (50) . cos (50)} =$ $y = (1 - cos (100))/(sin (100)) = (2sin^2 (50))/(2sin (50).cos (50)) =$
$= \frac{sin 50}{cos 50} = tan 50$ $= (sin 50)/(cos 50) = tan 50$

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How do you simplify $\frac{1 - cos 100}{sin 100}$ $(1-cos100)/sin100$ ?

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