Question

Find the value of the following:

cosec 15º

Answer 1

cosec 15º = `1/(sin 15^circ)`

Consider sin 15° = sin(45° – 30°)

= sin 45° cos 30° – cos 45° sin 30°

`= 1/sqrt2 xx sqrt3/2 - 1/sqrt2 xx 1/2`

`= sqrt3/(2sqrt2) - 1/(2sqrt2)`

`= (sqrt3 - 1)/(2sqrt2)`

cosec 15° = `1/(sin 15^circ) = (2sqrt2)/(sqrt3 - 1)`