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Question
Prove that 2 tan 80° = tan 85° – tan 5°.
Solution
Consider tan 80° = tan(85° – 5°)
`= (tan 85° - tan 5°)/(1 + tan 85° tan 5°)`
`= (tan 85° - tan 5°)/(1 + tan 85° tan (90° - 85°))`
`= (tan 85^circ - tan 5^circ)/(1 + tan 85^circ xx cot 85^circ)`
`= (tan 85^circ - tan 5^circ)/(1 + 1)`
`= (tan 85^circ - tan 5^circ)/2`
∴ 2 tan 80° = tan 85° – tan 5°
Hence Proved.
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