Ques:

Asked by sourabh7jain | 25th Jun, 2016, 10:21: AM

Expert Answer:

open vertical bar table row cell sin squared A end cell cell sin A cos A end cell cell cos squared A end cell row cell sin squared B end cell cell sin B cos B end cell cell cos squared B end cell row cell sin squared C end cell cell sin C cos C end cell cell cos squared C end cell end table close vertical bar
equals 1 half open vertical bar table row cell s i n squared A end cell cell 2 s i n A c o s A end cell cell c o s squared A end cell row cell s i n squared B end cell cell 2 s i n B c o s B end cell cell c o s squared B end cell row cell s i n squared C end cell cell 2 s i n C c o s C end cell cell c o s squared C end cell end table close vertical bar
A p p l y i n g space R subscript 1 rightwards arrow R subscript 1 minus R subscript 2 space a n d space R subscript 2 rightwards arrow R subscript 2 minus R subscript 3 comma space w e space g e t
equals 1 half open vertical bar table row cell s i n squared A minus sin squared B end cell cell sin 2 A minus sin 2 B end cell cell c o s squared A minus cos squared B end cell row cell s i n squared B minus sin squared C end cell cell sin 2 B minus sin 2 C end cell cell c o s squared B minus cos squared C end cell row cell s i n squared C end cell cell sin 2 C end cell cell c o s squared C end cell end table close vertical bar
equals 1 half open vertical bar table row cell sin open parentheses A plus B close parentheses sin open parentheses A minus B close parentheses end cell cell 2 sin open parentheses A minus B close parentheses cos open parentheses A plus B close parentheses end cell cell negative s i n open parentheses A plus B close parentheses s i n open parentheses A minus B close parentheses end cell row cell sin open parentheses B plus C close parentheses sin open parentheses B minus C close parentheses end cell cell 2 s i n open parentheses B minus C close parentheses c o s open parentheses B plus C close parentheses end cell cell negative s i n open parentheses B plus C close parentheses s i n open parentheses B minus C close parentheses end cell row cell sin squared C end cell cell sin 2 C end cell cell cos squared C end cell end table close vertical bar
equals 1 half sin open parentheses A minus B close parentheses sin open parentheses B minus C close parentheses open vertical bar table row cell sin open parentheses A plus B close parentheses end cell cell 2 cos open parentheses A plus B close parentheses end cell cell negative sin open parentheses A plus B close parentheses end cell row cell sin open parentheses B plus C close parentheses end cell cell 2 cos open parentheses B plus C close parentheses end cell cell negative sin open parentheses B plus C close parentheses end cell row cell sin squared C end cell cell sin 2 C end cell cell cos squared C end cell end table close vertical bar
A p p l y i n g space C subscript 1 rightwards arrow C subscript 1 plus C subscript 3 comma space w e space g e t
space 1 half s i n open parentheses A minus B close parentheses s i n open parentheses B minus C close parentheses open vertical bar table row 0 cell 2 c o s open parentheses A plus B close parentheses end cell cell negative s i n open parentheses A plus B close parentheses end cell row 0 cell 2 c o s open parentheses B plus C close parentheses end cell cell negative s i n open parentheses B plus C close parentheses end cell row 1 cell s i n 2 C end cell cell c o s squared C end cell end table close vertical bar
equals space 1 half s i n open parentheses A minus B close parentheses s i n open parentheses B minus C close parentheses open vertical bar table row 0 cell negative 2 c o s C end cell cell negative s i n C end cell row 0 cell negative 2 cos A end cell cell negative s i n A end cell row 1 cell s i n 2 C end cell cell c o s squared C end cell end table close vertical bar space left parenthesis sin c e space A plus B plus C equals straight pi right parenthesis
equals space 1 half s i n open parentheses A minus B close parentheses s i n open parentheses B minus C close parentheses open square brackets 2 cos C sin A minus 2 cos A sin C close square brackets
equals 1 half s i n open parentheses A minus B close parentheses s i n open parentheses B minus C close parentheses open square brackets 2 sin open parentheses A minus C close parentheses close square brackets
equals s i n open parentheses A minus B close parentheses s i n open parentheses B minus C close parentheses sin open parentheses A minus C close parentheses
equals negative s i n open parentheses A minus B close parentheses s i n open parentheses B minus C close parentheses sin open parentheses C minus A close parentheses

Answered by satyajit samal | 27th Jun, 2016, 12:27: PM