EVALUATE:
(cosec square 61_tan square 29+ 2×sin 30 /cosec square A_tan square (90_A+) + tan square 45)+(3 cot 11×cot21×cot31×cot 59×cot69×cot 79/2(sin square 21+sin square 69)-(cos square 41+cos square 49))

Asked by Sai Seravan Bodipudi | 6th Dec, 2014, 07:15: AM

Expert Answer:

G i v e n space e x p r e s s i o n space i s : fraction numerator cos e c squared 61 degree minus tan squared 29 degree plus 2 cross times sin 30 degree over denominator cos e c squared A minus tan squared open parentheses 90 minus A close parentheses plus tan squared 45 degree end fraction plus fraction numerator 3 c o t 11 degree cross times c o t 21 degree cross times c o t 31 degree cross times c o t 59 degree cross times c o t 69 degree cross times c o t 79 degree over denominator 2 open parentheses sin squared 21 degree plus sin squared 69 degree close parentheses minus open parentheses cos squared 41 degree plus cos squared 49 degree close parentheses end fraction equals fraction numerator cos e c squared open parentheses 90 minus 29 close parentheses degree minus tan squared 29 degree plus 2 cross times sin 30 degree over denominator cos e c squared A minus tan squared open parentheses 90 minus A close parentheses plus tan squared 45 degree end fraction plus fraction numerator 3 c o t open parentheses 90 minus 79 close parentheses degree cross times c o t open parentheses 90 minus 69 close parentheses degree cross times c o t open parentheses 90 minus 59 close parentheses degree cross times c o t 59 degree cross times c o t 69 degree cross times c o t 79 degree over denominator 2 open parentheses sin squared 21 degree plus sin squared open parentheses 90 minus 21 close parentheses degree close parentheses minus open parentheses cos squared 41 degree plus cos squared open parentheses 90 minus 41 close parentheses degree close parentheses end fraction equals fraction numerator s e c squared 29 degree minus tan squared 29 degree plus 2 cross times sin 30 degree over denominator s e c squared open parentheses 90 minus A close parentheses minus tan squared open parentheses 90 minus A close parentheses plus 1 end fraction plus fraction numerator 3 tan 79 degree cross times tan 69 degree cross times tan 59 degree cross times c o t 59 degree cross times c o t 69 degree cross times c o t 79 degree over denominator 2 open parentheses sin squared 21 degree plus cos squared 21 degree close parentheses minus open parentheses cos squared 41 degree plus sin squared 41 degree close parentheses end fraction equals fraction numerator 1 plus 2 cross times begin display style 1 half end style over denominator 1 plus 1 end fraction plus fraction numerator 3 cross times 1 cross times 1 cross times 1 over denominator 2 minus 1 end fraction equals fraction numerator 1 plus 1 over denominator 1 plus 1 end fraction plus fraction numerator 3 cross times 1 cross times 1 cross times 1 over denominator 2 minus 1 end fraction equals 2 over 2 plus 3 equals 1 plus 3 equals 4

Answered by Vimala Ramamurthy | 8th Dec, 2014, 10:03: AM