The value of 3 +2 2 3 +4 4 3 +8 8 3 is equal to

Step-by-step solution

Evaluating the expression 3 + 2 2 3 + 4 4 3 + 8 8 3 requires simplifying each term using trigonometric identities. Using the known value 3 = 3 , the first term is 3 . For the second term, 2 3 = ( - 3 ) = - 3 = - 3 , so 2 2 3 = -2 3 . The third term simplifies as 4 3 = ( + 3 ) = 3 = 3 , giving 4 4 3 = 4 3 . Finally, 8 3 = (2 + 2 3 ) = 2 3 = - 3 , so 8 8 3 = -8 3 . Combining all terms: 3 - 2 3 + 4 3 - 8 3 = (1 - 2 + 4 - 8) 3 = -5 3 . The final result is -5 3 .