Question

Prove the following:

tan10° + tan35° + tan10°.tan35° = 1

Answer 1

Since 45° = 10° + 35°,

tan 45° = tan (10° + 35°)

∴ 1 = `(tan10^circ + tan35^circ)/(1 - tan10^circ tan35^circ)`

∴ 1 – tan10° tan35° = tan10° + tan35°

∴ tan10° + tan35° + tan10° tan35° = 1