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Question
Prove the following:
tan10° + tan35° + tan10°.tan35° = 1
Solution
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
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