Consider the following statements in respect of the determinant | array cc ^2 2 & ^2 2 ^2 2 & ^2 2 array | where , are complementary angles 1. The value of the determinant is 1 2 ( - 2 ) . 2. The maximum value of the determinant is 1 2 . Which of the above statements is/ are correct?

Step-by-step solution

aligned & + =90^ & | array ll ^2 2 & ^2 2 ^2 2 & ^2 2 array | & = ^2 2 ^2 2 - ^2 2 ^2 2 & = & ( 2 2 + 2 2 ) ( 2 2 - 2 2 ) & = ( - ) 2 ( + ) 2 & = ( - ) 2 (90^ ) 2 = ( - ) 2 1 2 aligned Maximum value of ( - 2 ) is 1 . So maximum value of determinent is ( 1 2 ) So both 1 and 2 are correct.