If Cos(? + ?), cos ?, cos (?-?) are in HP then  cos?. Sec ?/2 = -----

Asked by VISHNU pillai | 10th May, 2014, 07:43: PM

Expert Answer:

I f space cos open parentheses theta plus alpha apostrophe close parentheses comma space cos theta space a n d space cos open parentheses theta minus alpha apostrophe close parentheses space b e space i n space H. P comma space t h e n  fraction numerator 2 over denominator cos theta end fraction equals fraction numerator 1 over denominator cos open parentheses theta plus alpha apostrophe close parentheses end fraction plus fraction numerator 1 over denominator cos open parentheses theta minus alpha apostrophe close parentheses end fraction  rightwards double arrow fraction numerator 2 over denominator cos theta end fraction equals fraction numerator cos open parentheses theta plus alpha apostrophe close parentheses plus cos open parentheses theta minus alpha apostrophe close parentheses over denominator cos open parentheses theta plus alpha apostrophe close parentheses cos open parentheses theta minus alpha apostrophe close parentheses end fraction  rightwards double arrow 2 cos open parentheses theta plus alpha apostrophe close parentheses cos open parentheses theta minus alpha apostrophe close parentheses equals cos theta open parentheses cos open parentheses theta plus alpha apostrophe close parentheses plus cos open parentheses theta minus alpha apostrophe close parentheses close parentheses  rightwards double arrow cos 2 theta plus cos 2 alpha apostrophe equals 2 cos squared theta cos alpha apostrophe  rightwards double arrow 2 cos squared theta minus 1 plus cos 2 alpha apostrophe equals 2 cos squared theta cos alpha apostrophe  rightwards double arrow 2 cos squared theta open parentheses cos alpha apostrophe minus 1 close parentheses equals cos 2 alpha apostrophe minus 1  rightwards double arrow 2 cos squared theta open parentheses minus 2 sin squared fraction numerator alpha apostrophe over denominator 2 end fraction close parentheses equals minus 2 s in squared alpha apostrophe  rightwards double arrow 2 cos squared theta open parentheses minus 2 sin squared fraction numerator alpha apostrophe over denominator 2 end fraction close parentheses equals minus 2 cross times 4 s in squared fraction numerator alpha apostrophe over denominator 2 end fraction cos squared fraction numerator alpha apostrophe over denominator 2 end fraction  rightwards double arrow cos squared theta equals 2 cos squared fraction numerator alpha apostrophe over denominator 2 end fraction  rightwards double arrow cos squared theta s e c squared fraction numerator alpha apostrophe over denominator 2 end fraction equals 2  rightwards double arrow cos theta s e c fraction numerator alpha apostrophe over denominator 2 end fraction equals plus-or-minus square root of 2

Answered by Avinash Soni | 13th May, 2014, 09:53: AM