SOLUTION: if sin + cosec =2 find sin^-7 + cos ^7

You are given that  +  = 2.    (1)

Obviously, (1) implies that sin(x) is positive. 


Let y = .   Then (1) becomes

 +  = 2,

which implies  - 2 +  = 0 =  = 0.


Hence,  =  and then y = 1.


Thus sin(x) = 1 and cos(x) = 0.


Now  +  = 1.