1e:["$","div",null,{"className":"p-6 md:p-8","children":["$","h1",null,{"className":" prose prose-lg max-w-none break-words prose-headings:font-bold prose-headings:text-slate-900 prose-p:text-slate-700 prose-p:leading-relaxed prose-strong:text-slate-900 prose-ul:list-disc prose-ol:list-decimal prose-li:text-slate-700 mb-4 [&_table]:w-auto [&_table]:max-w-full [&_table]:border-collapse [&_th]:border [&_th]:border-slate-300 [&_th]:px-3 [&_th]:py-2 [&_th]:text-left [&_td]:border [&_td]:border-slate-200 [&_td]:px-3 [&_td]:py-2 [&_table]:my-4 overflow-x-auto","dangerouslySetInnerHTML":{"__html":"

Prove that:

cot(x) × cot(2x) − cot(2x) × cot(3x) − cot(3x) × cot(x) = 1

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cot(3x) = cot(2x + x)

cot(3x) = (cot(2x) × cot(x) − 1) / (cot(x) + cot(2x))

cot(3x) × cot(x) + cot(3x) × cot(2x) = cot(2x) × cot(x) − 1

cot(x) × cot(2x) − cot(2x) × cot(3x) − cot(3x) × cot(x) = 1

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Prove that:cot(x) × cot(2x) − cot(2x) × cot(3x) − cot(3x) × cot(x) = 1

Verified Answer

Prove that:
cot(x) × cot(2x) − cot(2x) × cot(3x) − cot(3x) × cot(x) = 1