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Question
Prove the following:
`(cos15^circ - sin15^circ)/(cos15^circ + sin15^circ) = 1/sqrt(3)`
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Solution
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.
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