Find value of
(a)(1+tanA+secA)(1+cotA-cosecA)
(b)cosstraight pi over 7 minus cos fraction numerator 2 straight pi over denominator 7 end fraction plus cos fraction numerator 3 straight pi over denominator 7 end fraction

Asked by araima2001 | 24th Oct, 2015, 08:17: PM

Expert Answer:

left parenthesis a right parenthesis C o n s i d e r space t h e space e x p r e s s i o n comma space open parentheses 1 plus t a n A plus s e c A close parentheses open parentheses 1 plus c o t A minus c o s e c A close parentheses colon open parentheses 1 plus tan A plus s e c A close parentheses open parentheses 1 plus c o t A minus cos e c A close parentheses equals open parentheses 1 plus fraction numerator sin A over denominator cos A end fraction plus fraction numerator 1 over denominator cos A end fraction close parentheses open parentheses 1 plus fraction numerator cos A over denominator sin A end fraction minus fraction numerator 1 over denominator sin A end fraction close parentheses equals open parentheses fraction numerator cos A plus s i n A plus 1 over denominator c o s A end fraction close parentheses open parentheses fraction numerator sin A plus c o s A minus 1 over denominator s i n A end fraction close parentheses equals fraction numerator open parentheses c o s A plus s i n A plus 1 close parentheses open parentheses s i n A plus c o s A minus 1 close parentheses over denominator s i n A c o s A end fraction equals fraction numerator open parentheses c o s A plus s i n A close parentheses squared minus 1 squared over denominator s i n A c o s A end fraction equals fraction numerator c o s squared A plus s i n squared A plus 2 s i n A c o s A minus 1 over denominator s i n A c o s A end fraction equals fraction numerator 1 plus 2 s i n A c o s A minus 1 over denominator s i n A c o s A end fraction equals fraction numerator 2 s i n A c o s A over denominator s i n A c o s A end fraction equals 2
left parenthesis b right parenthesis W e space k n o w space t h a t comma c o s C minus c o s D equals 2 s i n fraction numerator C plus D over denominator 2 end fraction s i n fraction numerator D minus C over denominator 2 end fraction sin C minus sin D equals 2 cos fraction numerator C plus D over denominator 2 end fraction s i n fraction numerator C minus D over denominator 2 end fraction A l s o comma space w e space k n o w space t h a t space cos fraction numerator 5 straight pi over denominator 7 end fraction equals negative cos fraction numerator 2 straight pi over denominator 7 end fraction C o n s i d e r space t h e space e x p r e s s i o n comma space c o s straight pi over 7 minus c o s fraction numerator 2 straight pi over denominator 7 end fraction plus c o s fraction numerator 3 straight pi over denominator 7 end fraction colon c o s straight pi over 7 minus c o s fraction numerator 2 straight pi over denominator 7 end fraction plus c o s fraction numerator 3 straight pi over denominator 7 end fraction equals c o s straight pi over 7 plus space c o s fraction numerator 5 straight pi over denominator 7 end fraction plus c o s fraction numerator 3 straight pi over denominator 7 end fraction equals open square brackets cos straight pi over 7 plus space cos fraction numerator 5 straight pi over denominator 7 end fraction plus cos fraction numerator 3 straight pi over denominator 7 end fraction close square brackets cross times fraction numerator 2 sin straight pi over 7 over denominator 2 s i n straight pi over 7 end fraction equals open square brackets 2 s i n straight pi over 7 c o s straight pi over 7 plus space 2 s i n straight pi over 7 c o s fraction numerator 5 straight pi over denominator 7 end fraction plus 2 s i n straight pi over 7 c o s fraction numerator 3 straight pi over denominator 7 end fraction close square brackets cross times fraction numerator 1 over denominator 2 s i n straight pi over 7 end fraction equals open square brackets s i n fraction numerator 2 straight pi over denominator 7 end fraction plus space s i n open parentheses straight pi over 7 plus fraction numerator 5 straight pi over denominator 7 end fraction close parentheses plus space s i n open parentheses straight pi over 7 minus fraction numerator 5 straight pi over denominator 7 end fraction close parentheses plus space s i n open parentheses straight pi over 7 plus fraction numerator 3 straight pi over denominator 7 end fraction close parentheses plus space s i n open parentheses straight pi over 7 minus fraction numerator 3 straight pi over denominator 7 end fraction close parentheses close square brackets cross times fraction numerator 1 over denominator 2 s i n straight pi over 7 end fraction equals open square brackets s i n fraction numerator 2 straight pi over denominator 7 end fraction plus space s i n open parentheses fraction numerator 6 straight pi over denominator 7 end fraction close parentheses minus space s i n open parentheses fraction numerator 4 straight pi over denominator 7 end fraction close parentheses plus space s i n open parentheses fraction numerator 4 straight pi over denominator 7 end fraction close parentheses minus s i n open parentheses fraction numerator 2 straight pi over denominator 7 end fraction close parentheses close square brackets cross times fraction numerator 1 over denominator 2 s i n straight pi over 7 end fraction equals fraction numerator space s i n open parentheses fraction numerator 6 straight pi over denominator 7 end fraction close parentheses over denominator 2 s i n straight pi over 7 end fraction equals fraction numerator space s i n open parentheses straight pi minus straight pi over 7 close parentheses over denominator 2 s i n straight pi over 7 end fraction equals fraction numerator space s i n open parentheses straight pi over 7 close parentheses over denominator 2 s i n straight pi over 7 end fraction equals 1 half

Answered by Vimala Ramamurthy | 25th Oct, 2015, 03:10: PM

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