Which of the following is the correct option?

Asked by dineshchem108 | 3rd Sep, 2018, 09:03: AM

Expert Answer:

begin mathsize 16px style tan open parentheses straight alpha minus straight beta close parentheses equals fraction numerator sin 2 straight beta over denominator 3 minus cos 2 straight beta end fraction
tan open parentheses straight alpha minus straight beta close parentheses equals fraction numerator 2 sinβcosβ over denominator 2 minus 2 cos 2 straight beta plus 1 plus cos 2 straight beta end fraction
tan open parentheses straight alpha minus straight beta close parentheses equals fraction numerator begin display style 2 sinβcosβ end style over denominator begin display style 2 open parentheses 1 minus cos 2 straight beta close parentheses plus open parentheses 1 plus cos 2 straight beta close parentheses end style end fraction
tan open parentheses straight alpha minus straight beta close parentheses equals fraction numerator begin display style 2 sinβcosβ end style over denominator begin display style 2 cross times 2 sin squared straight beta plus 2 cos squared straight beta end style end fraction
tan open parentheses straight alpha minus straight beta close parentheses equals fraction numerator begin display style 2 sinβcosβ end style over denominator begin display style 4 sin squared straight beta plus 2 cos squared straight beta end style end fraction cross times fraction numerator begin display style fraction numerator 1 over denominator begin display style cos squared end style begin display style straight beta end style end fraction end style over denominator fraction numerator 1 over denominator begin display style cos squared straight beta end style end fraction end fraction
tan open parentheses straight alpha minus straight beta close parentheses equals fraction numerator begin display style 2 end style tan begin display style straight beta end style over denominator begin display style 4 end style begin display style tan squared end style begin display style straight beta end style begin display style plus end style begin display style 2 end style end fraction
tan open parentheses straight alpha minus straight beta close parentheses equals fraction numerator begin display style tan straight beta end style over denominator begin display style 2 tan squared straight beta plus 1 end style end fraction
fraction numerator begin display style tanα minus tanβ end style over denominator 1 plus tanαtanβ end fraction equals fraction numerator begin display style tanβ end style over denominator begin display style 2 tan squared straight beta plus 1 end style end fraction
Solving space further space we space get space correct space option space as space left parenthesis straight a right parenthesis. end style

Answered by Sneha shidid | 3rd Sep, 2018, 11:16: AM

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