If x^ 2^ 3^ . 88^ y^ =1 then (x+y)=

Step-by-step solution

The given equation is x^ 2^ 3^ 88^ y^ = 1 . Using the identity (90^ - ) = 1 , we can pair the terms in the product. Specifically, 2^ 88^ = 1 , 3^ 87^ = 1 , and so on. The product of terms from 2^ to 88^ involves pairs ( k^ (90^ - k^ )) = 1 . The middle term is 45^ = 1 . Thus, the product 2^ 3^ 88^ = 1 . Substituting this into the original equation, we get x^ 1 y^ = 1 , which implies x^ y^ = 1 . This can be rewritten as x^ = 1 y^ = y^ = (90^ - y^ ) . Therefore, x = 90 - y , which means x + y = 90^ . We need to find