Question

cos(π/16)+cos(3π/16)-------cos(13π/16)+cos(15π/16)
fine the value​

Answer 1

Answer:

cos⁡7π16=sin⁡(π2−7π16)=sin⁡π16" role="presentation" style="margin: 0px; padding: 0px; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">cos7π16=sin(π2−7π16)=sinπ16cos⁡7π16=sin⁡(π2−7π16)=sin⁡π16

cos⁡5π16=sin⁡(π2−5π16)=sin⁡3π16" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">cos5π16=sin(π2−5π16)=sin3π16cos⁡5π16=sin⁡(π2−5π16)=sin⁡3π16

cos⁡π16⋅cos⁡3π16⋅cos⁡5π16⋅cos⁡7π16" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">cosπ16⋅cos3π16⋅cos5π16⋅cos7π16cos⁡π16⋅cos⁡3π16⋅cos⁡5π16⋅cos⁡7π16

=cos⁡π16⋅cos⁡3π16⋅sin⁡3π16⋅sin⁡π16" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">=cosπ16⋅cos3π16⋅sin3π16⋅sinπ16=cos⁡π16⋅cos⁡3π16⋅sin⁡3π16⋅sin⁡π16

=14⋅(2cos⁡π16⋅sin⁡π16)⋅(2sin⁡3π16⋅cos⁡3π16)" role="presentation" style="margin: 0px; padding: 0px; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 15px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">=14⋅(2cosπ16⋅sinπ16)⋅(2sin3π16⋅cos3π16)=14⋅(2cos⁡π16⋅sin⁡π16)⋅(2sin⁡3π16⋅cos⁡3π16)

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