I f space tan space alpha equals fraction numerator a over denominator a plus 1 end fraction space a n d space tan space beta equals fraction numerator 1 over denominator 2 a plus 1 end fraction comma space f i n d space t h e space v a l u e space o f space alpha plus beta.

Asked by surajsubedi14 | 3rd Mar, 2015, 10:34: AM

Expert Answer:

tan open parentheses alpha plus beta close parentheses equals fraction numerator tan alpha plus tan beta over denominator 1 minus tan alpha cross times tan beta end fraction tan open parentheses alpha plus beta close parentheses equals fraction numerator begin display style fraction numerator a over denominator a plus 1 end fraction end style plus begin display style fraction numerator 1 over denominator 2 a plus 1 end fraction end style over denominator 1 minus fraction numerator a over denominator a plus 1 end fraction cross times fraction numerator 1 over denominator 2 a plus 1 end fraction end fraction tan open parentheses alpha plus beta close parentheses equals fraction numerator begin display style fraction numerator 2 a squared plus a plus a plus 1 over denominator open parentheses a plus 1 close parentheses open parentheses 2 a plus 1 close parentheses end fraction end style over denominator fraction numerator open parentheses a plus 1 close parentheses open parentheses 2 a plus 1 close parentheses minus a over denominator open parentheses a plus 1 close parentheses open parentheses 2 a plus 1 close parentheses end fraction end fraction tan open parentheses alpha plus beta close parentheses equals fraction numerator begin display style 2 a squared plus 2 a plus 1 end style over denominator 2 a squared plus 2 a plus 1 end fraction tan open parentheses alpha plus beta close parentheses equals 1 alpha plus beta equals tan to the power of negative 1 end exponent open parentheses 1 close parentheses equals straight pi over 4

Answered by Vijaykumar Wani | 3rd Mar, 2015, 10:55: AM

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