सही विकल्प चुनिए और अपने विकल्प की पुष्टि कीजिए:
$space fraction numerator 1 plus tan squared straight A over denominator 1 plus cot squared straight A end fraction$ बराबर हैं:

$sec squared straight A$

-1

cot²A

tan²A

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Solution

tan²A

fraction numerator 1 plus tan squared straight A over denominator 1 plus cot squared straight A end fraction space equals space fraction numerator sec squared straight A over denominator cosec squared straight A end fraction

equals space fraction numerator begin display style fraction numerator 1 over denominator cos squared straight A end fraction end style over denominator begin display style fraction numerator 1 over denominator sin squared straight A end fraction end style end fraction space equals space fraction numerator 1 over denominator cos squared straight A end fraction cross times fraction numerator sin squared straight A over denominator 1 end fraction

equals space fraction numerator sin squared straight A over denominator cos squared straight A end fraction space equals space tan squared straight A.

अत: विकल्प (D) सही हैं।

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