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Grade 12Trigonometry

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

Arushi Singh

12 Years agoGrade 12

1 Answer

Arun Kumar

Approved Tutor Answer12 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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