Question

доказать тождество:
 
1)   sin^4-cos^4+2cos^2=1

       2) cos/1-sin=1+sin/cos

Answer 1

1) $(sin^{2} - cos^{2} )( sin^{2} + cos^{2} )+2 cos^{2} =1$
$sin^{2} - cos^{2} +2 cos^{2} =1$
$sin^{2} + cos^{2} =1$
1=1

2)$frac{cos}{1-sin} = frac{1+sin}{cos}$
$frac{ cos^{2} }{cos(1-sin)} = frac{1- sin^{2} }{cos(1-sin)}$
$frac{ cos^{2} }{cos(1-sin)} = frac{ cos^{2} }{cos(1-sin)}$