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Prove that cot(A + B) = ABABcotAcotB-1cotA+cotB

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प्रश्न

Prove that cot(A + B) = `(cot "A" cot "B" - 1)/(cot "A" + cot "B")`

बेरीज
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उत्तर

cot(A + B) = `1/(tan("A" + "B"))`

= `1/((tan "A" + tan "B")/(1 - tan "A" tan "B"))`

= `(1 - tan"A" tan"B")/(tan"A" + tan "B")`

= `(1 - 1/cot"A" * 1/cot"B")/(1/cot "A" + 1/cot"B")`

= `((cot"A" cot"B" - 1)/(cot"A" cot"B"))/((cot"B" + cot"A")/(cot"A" cot"B"))`

cot(A + B) = `(cot"A" cot"B" - 1)/(cot"A" + cot"B")`

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Trigonometric Functions and Their Properties
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Trigonometry - Exercise 3.4 [पृष्ठ ११०]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
पाठ 3 Trigonometry
Exercise 3.4 | Q 21 | पृष्ठ ११०

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