Question

for which acute angle cos theta/1-sinx. + cosx/1+sinx=4... Is true ......x is theta .

Answer 1

Take the L.C.M.
$\frac{2cos(x)}{1-sin^{2}(x)}=4$
After simplifying L.H.S. you get cos(x)=½ then x=60°.

Answer 2

Take the L.C.M.  After simplifying L.H.S. you get cos(x)=½ then x=60°.