If = 1 3 , then what is the value of ( 2 ) ( 3 2 ) ?

Step-by-step solution

Using the trigonometric identity 2 A B = (A-B) - (A+B) , we have: ( 2 ) ( 3 2 ) = 1 2 [ ( 3 2 - 2 ) - ( 3 2 + 2 ) ] = 1 2 [ - (2 )] Using the double angle formula (2 ) = 2 ^2 - 1 , we get: (2 ) = 2 ( 1 3 )^2 - 1 = 2 9 - 1 = - 7 9 Substituting the values of and (2 ) : ( 2 ) ( 3 2 ) = 1 2 [ 1 3 - (- 7 9 ) ] = 1 2 [ 3 9 + 7 9 ] = 1 2 [ 10 9 ] = 5 9 Answer: 5 9