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प्रश्न
Prove the following:
`(cos27^circ + sin27^circ)/(cos27^circ - sin27^circ)` = tan72°
उत्तर
L.H.S. = `(cos27^circ + sin27^circ)/(cos27^circ - sin27^circ)`
= `((cos27^circ)/(cos27^circ) + (sin27^circ)/(cos27^circ))/((cos27^circ)/(cos27^circ) - (sin27^circ)/(cos27^circ))`
= `(1 + tan27^circ)/(1 - tan27^circ)`
= `(tan45^circ + tan27^circ)/(1 - tan45^circ xx tan27^circ)` ...[∵ tan45° = 1]
= tan(45° + 27°)
= tan72°
= R.H.S.
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