cot2cot12cot22cot32cot42cot45cot58cot68cot78cot88 Evaluate

Asked by RAHUL rd | 9th Sep, 2014, 08:10: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e x p r e s s i o n : c o t 2 cross times c o t 12 cross times c o t 22 cross times c o t 32 cross times c o t 42 cross times c o t 45 cross times c o t 48 cross times c o t 58 cross times c o t 68 cross times c o t 78 cross times c o t 88 equals fraction numerator cos 2 cross times cos 12 cross times cos 22 cross times cos 32 cross times cos 42 cross times cos 45 cross times cos 48 cross times cos 58 cross times cos 68 cross times cos 78 cross times cos 88 over denominator sin 2 cross times sin 12 cross times sin 22 cross times sin 32 cross times sin 42 cross times sin 45 cross times sin 48 cross times sin 58 cross times sin 68 cross times sin 78 cross times sin 88 end fraction R e w r i t i n g space t h e space a b o v e space a s comma c o t 2 cross times c o t 12 cross times c o t 22 cross times c o t 32 cross times c o t 42 cross times c o t 45 cross times c o t 48 cross times c o t 58 cross times c o t 68 cross times c o t 78 cross times c o t 88 equals fraction numerator open parentheses cos 2 cross times cos 88 close parentheses cross times open parentheses cos 12 cross times cos 78 close parentheses cross times open parentheses cos 22 cross times cross times cos 68 close parentheses cross times open parentheses cos 32 cross times cos 58 close parentheses cross times open parentheses cos 42 cross times cos 48 close parentheses cross times cos 45 over denominator open parentheses sin 2 cross times sin 88 close parentheses cross times open parentheses sin 12 cross times sin 78 close parentheses cross times open parentheses sin 22 cross times cross times sin 68 close parentheses cross times open parentheses sin 32 cross times sin 58 close parentheses cross times open parentheses sin 42 cross times sin 48 close parentheses cross times sin 45 end fraction W e space k n o w space t h a t comma cos u cross times cos v equals 1 half open square brackets cos open parentheses u minus v close parentheses plus cos open parentheses u plus v close parentheses close square brackets a n d sin u cross times sin v equals 1 half open square brackets cos open parentheses u minus v close parentheses minus cos open parentheses u plus v close parentheses close square brackets T h u s comma space w e space h a v e comma c o t 2 cross times c o t 12 cross times c o t 22 cross times c o t 32 cross times c o t 42 cross times c o t 45 cross times c o t 48 cross times c o t 58 cross times c o t 68 cross times c o t 78 cross times c o t 88 equals fraction numerator open parentheses cos 2 cross times cos 88 close parentheses cross times open parentheses cos 12 cross times cos 78 close parentheses cross times open parentheses cos 22 cross times cross times cos 68 close parentheses cross times open parentheses cos 32 cross times cos 58 close parentheses cross times open parentheses cos 42 cross times cos 48 close parentheses cross times cos 45 over denominator open parentheses sin 2 cross times sin 88 close parentheses cross times open parentheses sin 12 cross times sin 78 close parentheses cross times open parentheses sin 22 cross times cross times sin 68 close parentheses cross times open parentheses sin 32 cross times sin 58 close parentheses cross times open parentheses sin 42 cross times sin 48 close parentheses cross times sin 45 end fraction equals fraction numerator open square brackets begin display style fraction numerator cos 86 plus cos 90 over denominator 2 end fraction end style close square brackets cross times open square brackets fraction numerator cos 66 plus cos 90 over denominator 2 end fraction close square brackets cross times open square brackets fraction numerator cos 46 plus cos 90 over denominator 2 end fraction close square brackets cross times open square brackets fraction numerator cos 26 plus cos 90 over denominator 2 end fraction close square brackets cross times open square brackets fraction numerator cos 6 plus cos 90 over denominator 2 end fraction close square brackets over denominator open square brackets fraction numerator cos 86 minus cos 90 over denominator 2 end fraction close square brackets cross times open square brackets fraction numerator cos 66 minus cos 90 over denominator 2 end fraction close square brackets cross times open square brackets fraction numerator cos 46 minus cos 90 over denominator 2 end fraction close square brackets cross times open square brackets fraction numerator cos 26 minus cos 90 over denominator 2 end fraction close square brackets cross times open square brackets fraction numerator cos 6 minus cos 90 over denominator 2 end fraction close square brackets end fraction cross times c o t 45 equals fraction numerator open square brackets begin display style fraction numerator cos 86 over denominator 2 end fraction end style close square brackets cross times open square brackets fraction numerator cos 66 over denominator 2 end fraction close square brackets cross times open square brackets fraction numerator cos 46 over denominator 2 end fraction close square brackets cross times open square brackets fraction numerator cos 26 over denominator 2 end fraction close square brackets cross times open square brackets fraction numerator cos 6 over denominator 2 end fraction close square brackets over denominator open square brackets fraction numerator cos 86 over denominator 2 end fraction close square brackets cross times open square brackets fraction numerator cos 66 over denominator 2 end fraction close square brackets cross times open square brackets fraction numerator cos 46 over denominator 2 end fraction close square brackets cross times open square brackets fraction numerator cos 26 over denominator 2 end fraction close square brackets cross times open square brackets fraction numerator cos 6 over denominator 2 end fraction close square brackets end fraction cross times c o t 45 equals 1

Answered by Vimala Ramamurthy | 10th Sep, 2014, 10:12: AM