Question

How do you simplify `(sin80°-sin10°) / (sin80°+ sin10°)`?

Answer 1

`(sin 80^@ - sin 10^@)/(sin 80^@ + sin 10^@) = tan 35^@`

Explanation:

`sin a ± sin b = 2 sin ((a±b)/2) cos ((a∓b)/2)`
`tan A = sin A/cos A`

`(sin 80^@ - sin 10^@)/(sin 80^@ + sin 10^@) = sin 35^@ cos 45^@/(sin 45^@cos 35^@) = tan 35^@/(tan 45^@) = tan 35^@`