Question

Sa se demonstreze egalitatea :

Answer 1

$(1+tgx)cos^{3}x+(1+ctgx)sin^{3}x=sinx+cosx$
$(1+\frac{sinx}{cosx} )cos^{3}x+(1+\frac{cosx}{sinx} )sin^{3}x=sinx+cosx$
$(cosx+sinx)cos^{2}x+(sinx+cosx)sin^{2}x=sinx+cosx$
$(cosx+sinx)cos^{2}x+(sinx+cosx)sin^{2}x=sinx+cosx |:(sinx+cosx)$
$cos^{2}x+sin^{2}x=1$