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1+(1-tan theta/1-cot theta)^2=sec^2

Asked by devanshbajpai078 | 03 Mar, 2019, 07:53: AM

Expert Answer

begin mathsize 12px style L H S thin space equals space 1 plus open parentheses fraction numerator 1 minus tan space theta over denominator 1 minus c o t space theta end fraction close parentheses squared space equals space fraction numerator open parentheses 1 space minus space c o t space theta close parentheses squared plus open parentheses 1 space minus space tan space theta close parentheses squared over denominator open parentheses 1 space minus space c o t space theta close parentheses squared end fraction space equals space fraction numerator 1 minus 2 c o t space theta plus space c o t squared theta space plus space 1 minus 2 space tan space theta plus space tan squared theta over denominator open parentheses 1 space minus space c o t space theta close parentheses squared end fraction L H S space equals space fraction numerator 2 space minus space 2 c o t space theta space minus space 2 space tan space theta space plus space c o t squared theta space plus space tan squared theta over denominator 1 minus space 2 space c o t space theta space plus space c o t squared theta end fraction cross times fraction numerator tan squared space theta over denominator tan squared theta end fraction L H S space equals space fraction numerator 2 space tan squared theta space minus space 2 space tan space theta space minus space 2 space tan cubed theta space plus space 1 space plus space tan to the power of 4 theta over denominator tan squared theta space minus 2 space tan space theta space plus 1 end fraction L H S space equals space fraction numerator tan to the power of 4 theta space minus space 2 tan cubed theta space plus space tan squared theta space plus space tan squared theta space minus space 2 space tan space theta space plus 1 over denominator tan squared theta space minus 2 space tan space theta space plus 1 end fraction space equals space fraction numerator tan squared theta open parentheses tan squared theta space minus 2 space tan space theta space plus 1 close parentheses plus tan squared theta space minus 2 space tan space theta space plus 1 over denominator tan squared theta space minus 2 space tan space theta space plus 1 end fraction L H S space equals space fraction numerator open parentheses 1 plus space tan squared theta close parentheses open parentheses tan squared theta space minus 2 space tan space theta space plus 1 close parentheses over denominator open parentheses tan squared theta space minus 2 space tan space theta space plus 1 close parentheses end fraction space equals space 1 plus space tan squared theta space equals space s e c squared theta end style

Answered by Thiyagarajan K | 03 Mar, 2019, 12:45: PM

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