If tan 20º =then show that
tan 160° - tan 110° 1-22
1+tan 160° tan 110° 22
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Answer:
Given tan 20°=λ
tan 40°=tan2(20°) = 2tan 20° / 1 - tan²20° = 2λ / 1-λ²
LHS = tan160° - tan110°/1+ tan 160° tan110° = tan ( 160°-110°)
= tan 50° tan(90° - 40°) cot 40° = 1/tan40°
= 1-λ² / 2λ = RHS
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