Question

Prove the following:

`(cos15^circ - sin15^circ)/(cos15^circ + sin15^circ) = 1/sqrt(3)`

Answer 1

L.H.S. = `(cos15^circ - sin15^circ)/(cos15^circ + sin15^circ)`

Dividing numerator and denominator by cos15°, we get

L.H.S. = `(1 - (sin15^circ)/(cos15^circ))/(1 + (sin15^circ)/(cos15^circ))`

= `(1 - tan15^circ)/(1 + tan15^circ)`

= `(tan45^circ - tan15^circ)/(1 + (tan45^circ)(tan15^circ))` ...[∵ tan 45° = 1]

= tan(45° – 15°)

= tan30°

= `1/sqrt(3)`

= R.H.S.