Solve the following system of simultaneous equation for `xa n dydot` `4^(sinx)+3^(1//cosy)=11` `5x16^(sinx)-2x3^(1//cosy)=2`

Explanation

Let `4^(sin x)=u and 3^(1//cos y)=v` .
Then, the given system of equations reduces to
`u+v=11` ...(i)
`5u^(2) -2v=2` ...(ii)
Eliminating v from (i) and (ii), we get
`5u^(2) -22+2u =2`
or `(5u+12) (u-2)=0`
or `u-2=0" "[ :' u=4^(sin x) gt 0" for all "x, :. 5u+12 gt 0]`
or `4^(sin x)=2`
or `2 sin x=1`
or `sin x=1/2`
or `sin x="sin" pi/6`
or `x=npi+(-1)^(n) pi/6, n in Z`
Putting the value of u in (i), we get `v=9`
or `3^(1//cos y)=3^(2)`
or `cos y =1/2`
or `cos y= "cos" pi/3`
`y=2m pi pm pi/3, n in Z`
Hence, `x=n pi+(-1)^(n) pi/6` and `y=2 m pi pm pi/3`, where `m, n in Z`.