The value of the expression 2 ( s i n 1 ° + s i n 2 ° + s i n 3 ° + . . . . . . . . + s i n 89 ° ) 2 ( c o s 1 ° + c o s 2 ° + c o s 3 ° + . . . . . . . . + c o s 44 ° ) + 1 is equal to

Step-by-step solution

2 s i n 1 o + s i n 89 o + s i n 2 o + s i n 88 o + . . . . . . . + s i n 44 o + s i n 46 o + s i n 45 o 2 c o s 1 o + c o s 2 o + c o s 3 o + . . . . . . . + c o s 44 o + 1 = 2 2 s i n 45 o c o s 44 o + c o s 43 o + . . . . . . . + c o s 1 o + s i n 45 o 2 c o s 1 o + c o s 2 o + c o s 3 o + . . . . . . . + c o s 44 o + 1 = 2 s i n 45 o 2 c o s 1 o + c o s 2 o + . . . . . . . + c o s 44 o + 1 2 c o s 1 o + c o s 2 o + . . . . . . . + c o s 44 o + 1 = 2 ⋅ 1 2 = 2