If `sin^4alpha+cos^4beta+2=4sinalphacosbeta,0lt=alpha,betalt=pi/2` then find the value of `(sinalpha+cosbeta)dot`

Explanation

`sin^4alpha+sin^4beta +2 = 4sinalphacosbeta`

We can write the above equation as,

`(sin^2alpha - 1)^2 +(cos^2beta -1)^2+(sinalpha-cosbeta)^2 = 0`

`=>sin^2 alpha = 1 and cos^2beta = 1 and sinalpha = sinbeta`

As, `alpha and beta` in between `0` and `pi/2`,

`:. sinalpha= cosbeta = 1`

`:. sinalpha+ cos beta = 1+1 `

`=> sinalpha+ cos beta = 2. `