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[tex](1 - tg \alpha )^2 +(1 +tg \alpha )^2 = \frac {2}{cos ^2 \alpha}[/tex]
[tex]1 \cancel {- 2 tg \alpha} + tg ^2 \alpha + 1 \cancel {+ 2 tg \alpha} + tg ^2 \alpha= 2+ 2 tg ^2 \alpha = 2 (1 + tg^2 \alpha)= 2 (1 + \frac {sin^2 \alpha}{cos ^2 \alpha })=[/tex]
[tex]=2 (\frac {cos ^2 \alpha }{cos ^2 \alpha } + \frac {sin^2 \alpha}{cos ^2 \alpha })=2 . \frac {1 }{cos ^2 \alpha }[/tex]


[tex](1 - cotg \alpha )^2 +(1 + cotg \alpha )^2 = \frac {2}{sin ^2 \alpha}[/tex]
[tex]1 \cancel {- 2 cotg \alpha} + cotg ^2 \alpha + 1 \cancel {+ 2 cotg \alpha} + cotg ^2 \alpha= 2+ 2 cotg ^2 \alpha = 2 (1 + cotg^2 \alpha)= 2 (1 + \frac {cos ^2 \alpha }{sin^2 \alpha})=[/tex]
[tex]=2 (\frac {sin ^2 \alpha }{sin ^2 \alpha } + \frac {cos ^2 \alpha }{sin^2 \alpha})=2 . \frac {1 }{sin ^2 \alpha }[/tex]