Please solve the following question:
 
tan squared straight pi divided by 16 plus tan squared 2 straight pi divided by 16 plus...... plus tan squared 6 straight pi divided by 16 plus tan squared 7 straight pi divided by 16 equals straight k. space Find space value space of space straight k.

Asked by manasd | 28th Oct, 2015, 10:04: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e x p r e s s i o n colon tan squared straight pi over 16 plus t a n squared fraction numerator 2 straight pi over denominator 16 end fraction plus t a n squared fraction numerator 3 straight pi over denominator 16 end fraction plus t a n squared fraction numerator 4 straight pi over denominator 16 end fraction plus t a n squared fraction numerator 5 straight pi over denominator 16 end fraction plus t a n squared fraction numerator 6 straight pi over denominator 16 end fraction plus t a n squared fraction numerator 7 straight pi over denominator 16 end fraction equals k W e space k n o w space t h a t space tan squared A equals fraction numerator 1 minus cos 2 A over denominator 1 plus cos 2 A end fraction A l s o comma space w e space h a v e comma t a n squared fraction numerator 7 straight pi over denominator 16 end fraction equals t a n squared open parentheses straight pi over 2 minus straight pi over 16 close parentheses t a n squared fraction numerator 6 straight pi over denominator 16 end fraction equals t a n squared open parentheses straight pi over 2 minus fraction numerator 2 straight pi over denominator 16 end fraction close parentheses t a n squared fraction numerator 5 straight pi over denominator 16 end fraction equals t a n squared open parentheses straight pi over 2 minus fraction numerator 3 straight pi over denominator 16 end fraction close parentheses  R e w r i t i n g space t h e space g i v e n space e x p r e s s i o n comma space w e space h a v e comma t a n squared straight pi over 16 plus t a n squared fraction numerator 2 straight pi over denominator 16 end fraction plus t a n squared fraction numerator 3 straight pi over denominator 16 end fraction plus t a n squared fraction numerator 4 straight pi over denominator 16 end fraction plus t a n squared fraction numerator 5 straight pi over denominator 16 end fraction plus t a n squared fraction numerator 6 straight pi over denominator 16 end fraction plus t a n squared fraction numerator 7 straight pi over denominator 16 end fraction equals t a n squared straight pi over 16 plus t a n squared fraction numerator 7 straight pi over denominator 16 end fraction plus t a n squared f</h3>
					<div class=

Answered by Vimala Ramamurthy | 29th Oct, 2015, 11:57: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.