Айниятро исбот кунед:
\((1+\frac{1}{\cos{2\alpha}}+\operatorname{tg}{2\alpha})(1-\frac{1}{\cos{2\alpha}}+\operatorname{tg}{2\alpha})=\)
\( = 2\operatorname{tg}{2\alpha}\)
\(A = (1+\frac{1}{\cos{2\alpha}}+\operatorname{tg}{2\alpha})(1-\frac{1}{\cos{2\alpha}}+\operatorname{tg}{2\alpha})\)
\(B = 2\operatorname{tg}{2\alpha}\)
\(A =((1+\operatorname{tg}{2\alpha})+\frac{1}{\cos{2\alpha}})((1+\operatorname{tg}{2\alpha})-\frac{1}{\cos{2\alpha}})=\)
\( = (1+\operatorname{tg}{2\alpha})^2-(\frac{1}{\cos{2\alpha}})^2\)
\(A = 1+2\operatorname{tg}{2\alpha}+\operatorname{tg}^2{2\alpha}-\frac{1}{\cos^2{2\alpha}}\)
\(1+\operatorname{tg}^2{2\alpha} = \frac{1}{\cos^2{2\alpha}}\)
\(A = 2\operatorname{tg}{2\alpha}+\frac{1}{\cos^2{2\alpha}}-\frac{1}{\cos^2{2\alpha}} = 2\operatorname{tg}{2\alpha}\)
\(A = 2\operatorname{tg}{2\alpha}\)
Исбот шуд.