Question

How do you simplify `(1-cos100)/sin100`?

Answer 1

tan (50)

Explanation:

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