1-sin^2a+3cos^2a; 1/sin^2a-ctg^2a

Вспомним основное тригонометрическое тождество:
$\cos^2{\alpha} + \sin^2{\alpha} = 1$

1)
$1 - \sin^2{\alpha} +3 \cos^2{\alpha} = \sin^2{\alpha} + \cos^2{\alpha} - \sin^2{\alpha} +3 \cos^2{\alpha} = 4 \cos^2{\alpha}$

2)
$\dfrac{1}{\sin^2{\alpha}} - \text{ctg}^2{\alpha} = \dfrac{1}{\sin^2{\alpha}} - \dfrac{\cos^2{\alpha}}{\sin^2{\alpha}} = \dfrac{1 - \cos^2{\alpha}}{\sin^2{\alpha}} = \dfrac{\sin^2{\alpha}}{\sin^2{\alpha}} = 1$