how P r o v e : cos 5 pi divided by 12 equals left parenthesis square root of 3 minus 1 right parenthesis divided by 2 square root of 2

Asked by Shubham Kumar | 9th Nov, 2014, 11:15: AM

Expert Answer:

W e space k n o w space t h a t space fraction numerator 5 straight pi over denominator 12 end fraction equals straight pi over 6 plus straight pi over 4 T h u s comma space cos fraction numerator 5 straight pi over denominator 12 end fraction equals cos open parentheses straight pi over 6 plus straight pi over 4 close parentheses rightwards double arrow cos fraction numerator 5 straight pi over denominator 12 end fraction equals cos straight pi over 6 cross times cos straight pi over 4 minus sin straight pi over 6 cross times sin straight pi over 4 rightwards double arrow cos fraction numerator 5 straight pi over denominator 12 end fraction equals fraction numerator square root of 3 over denominator 2 end fraction cross times fraction numerator square root of 2 over denominator 2 end fraction minus 1 half cross times fraction numerator square root of 2 over denominator 2 end fraction rightwards double arrow cos fraction numerator 5 straight pi over denominator 12 end fraction equals fraction numerator square root of 6 over denominator 4 end fraction minus fraction numerator square root of 2 over denominator 4 end fraction rightwards double arrow cos fraction numerator 5 straight pi over denominator 12 end fraction equals fraction numerator square root of 6 minus square root of 2 over denominator 4 end fraction rightwards double arrow cos fraction numerator 5 straight pi over denominator 12 end fraction equals fraction numerator square root of 2 cross times square root of 3 minus square root of 2 over denominator 2 cross times square root of 2 cross times square root of 2 end fraction rightwards double arrow cos fraction numerator 5 straight pi over denominator 12 end fraction equals fraction numerator square root of 2 cross times open parentheses square root of 3 minus 1 close parentheses over denominator 2 cross times square root of 2 cross times square root of 2 end fraction rightwards double arrow cos fraction numerator 5 straight pi over denominator 12 end fraction equals fraction numerator open parentheses square root of 3 minus 1 close parentheses over denominator 2 square root of 2 end fraction

Answered by Vimala Ramamurthy | 9th Nov, 2014, 02:48: PM