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a)$1+tan^2 \alpha = 1+ \dfrac{sin^2 \alpha}{cos^2 \alpha}$
$=1+ \dfrac{1-cos^2 \alpha}{cos^2 \alpha}$
$=1+\dfrac{1}{cos^2 \alpha}-1$
$=\dfrac{1}{cos^2 \alpha}$( đpcm)
b)$1+cot^2 \alpha= \dfrac{1}{sin^2 \alpha}$
$1+cot^2 \alpha= 1+\dfrac{cos^2 \alpha}{sin^2 \alpha}=\dfrac{cos^2 \alpha +sin^2 \alpha}{sin^2 \alpha} =\dfrac{1}{sin^2 \alpha}$