Question

tan70°+tan 50°+tan 10°​

Answer 1

Answer:

Consider tanx+tan(x+60∘)+tan(x+120∘), then

Step-by-step explanation:

tanx+tan(x+60∘)+tan(x+120∘)=tanx+tanx+tan60∘1−tanxtan60∘+tanx+tan120∘1−tanxtan120∘=tanx+tanx+3–√1−3–√tanx+tanx−3–√1+3–√tanx=tanx+tanx+3–√tan2x+3–√+3tanx1−3tan2x+tanx−3–√tan2x−3–√+3tanx1−3tan2x=tanx(1−3tan2x)1−3tan2x+8tanx1−3tan2x=9tanx−3tan33x1−3tan2x=3(3tanx−tan33x1−3tan2x)=3tan3x