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Prove cot a + cot(60+a)-cot(60-a)=3 cot3a

Prove
cot a + cot(60+a)-cot(60-a)=3 cot3a

Grade:12

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
6 years ago
Hello Student,
\\ \\cot a + cot(60+a)-cot(60-a)=3 cot3a \\=cot a+{cos(60+a) \over sin(60+a)}-{cos(60-a) \over sin(60-a)} \\=cota+{cosA-\sqrt3sinA \over \sqrt3cosA+sinA}-{cosA+\sqrt3sinA \over \sqrt3cosA-sinA} \\=>cotA+{-8sinAcosA \over 3cos^2A-sin^2A} \\=>cotA-{8cotA \over 3cot^2A-1} \\cot a + cot(60+a)-cot(60-a)=3 cot3a \\=>{3cot^3A-9cotA \over 3cot^2A-1} \\=>3({cot^3A-3cotA \over 3cot^2A-1}) \\=>3cot3A \\
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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