Question

упростите выражении
а)
$tg \alpha - ctg \alpha - 1 =$
б)
$sin \^{2} \alpha + \cos ^{2} \alpha + tg^{2} \alpha$
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Answer 1

$a)\ \ tga-ctga-1=\dfrac{sina}{cosa}-\dfrac{cosa}{sina}-1=\dfrac{sin^2a-cos^2a}{sina\cdot cosa}-1=\\\\\\=\dfrac{-cos2a}{\frac{1}{2}\, sin2a}-1=-2\cdpot ctg2a-1$

$b)\ \ \underbrace {sin^2a+cos^2a}_{1}+tg^2a=1+tg^2a=1+\dfrac{sin^2a}{cos^2a}=\dfrac{sin^2a+cos^2a}{cos^2a}=\dfrac{1}{cos^2a}$