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CBSE Class 11-science Answered

Prove that : cot θ cot 2θ + cot 2θ cot 3θ + 2=cot θ (cot θ-cot 3θ )
Asked by tps.mjmdr | 16 Jun, 2018, 08:08: PM
answered-by-expert Expert Answer
begin mathsize 16px style cot space open parentheses straight A minus straight B close parentheses equals fraction numerator cot space straight A. cot space straight B plus 1 over denominator cot space straight B minus space cot space straight A end fraction
cot space straight A. space cot space straight B space equals space cot space open parentheses straight A minus straight B close parentheses open parentheses cot space straight B minus space cot space straight A close parentheses minus 1
now
LHS
equals bottom enclose cot space straight theta space cot space 2 straight theta end enclose space plus space bottom enclose cot space 2 straight theta space cot space 3 straight theta end enclose space plus space 2
equals cot open parentheses straight theta minus 2 straight theta close parentheses open parentheses cot space 2 straight theta minus cotθ close parentheses minus 1 plus cot open parentheses 2 straight theta minus 3 straight theta close parentheses open parentheses cot space 3 straight theta minus cot 2 straight theta close parentheses minus 1 plus 2
equals cot open parentheses straight theta minus 2 straight theta close parentheses open parentheses cot space 2 straight theta minus cotθ close parentheses plus cot open parentheses 2 straight theta minus 3 straight theta close parentheses open parentheses cot space 3 straight theta minus cot 2 straight theta close parentheses
equals cot open parentheses negative straight theta close parentheses open parentheses cot space 2 straight theta minus cotθ close parentheses plus cot open parentheses negative straight theta close parentheses open parentheses cot space 3 straight theta minus cot 2 straight theta close parentheses
equals cot open parentheses negative straight theta close parentheses. cot space 2 straight theta minus cot open parentheses negative straight theta close parentheses. cotθ plus cot open parentheses negative straight theta close parentheses. cot space 3 straight theta minus cot open parentheses negative straight theta close parentheses. cot 2 straight theta
equals negative cot open parentheses negative straight theta close parentheses. cotθ plus cot open parentheses negative straight theta close parentheses. cot space 3 straight theta
equals cot open parentheses straight theta close parentheses. cotθ minus cot open parentheses straight theta close parentheses. cot space 3 straight theta end style
Answered by Arun | 19 Jun, 2018, 11:19: AM

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