In `Delta ABC,if cos A+sin A-2/(cosB+sin B)=0,` then the value of `((a+b)/c)^4` is

Answer

4

Explanation

`cos A + sin A - (2)/(cos B + sin B) = 0`
or `cos A cos B + sin A sin B + cos A sin B + sin A cos B = 2`
or `cos (A -B) + sin (A +B) =2`
or `cos (A -B) = 1 and sin (A +B) = 1`
`rArr A = B, "so " a = b and sin 2A = 1`
`rArr A = 45^(@)`
Hence, `(a+b)/(c) = (2a)/(asqrt2) = sqrt2`