Write the trigonometric expression as an algebraic expression in u and v . assume that the variables u and v represent positive real numbers. sin−cos−1utan−1v

Sorry, Jamie, but your expression    sin−cos−1utan−1v    is not properly formed.  "sin" and "cos" never stand alone; they MUST each have an argument:

sin x, cos x:  OK

sin - cos   definitely NOT OK.

Please go back and take a careful look at the original problem.  Then ensure you copy that original problem exactly to form a proper question here.