Question

resolver
cot^2x(1+tan^2x)=csc^2x
1-2 sen^2x=1-tan^2x/1+tan^2x

Answer 1

$cot^{2}x(1+tan^{2}x)=csc^{2}x \\ \frac{cos^{2}x}{sen^{2}x}(1+\frac{sen^{2}x}{cos^{2}x})=csc^{2}x\\ \frac{cos^{2}x}{sen^{2}x}+\frac{cos^{2}x}{sen^{2}x}*\frac{sen^{2}x}{cos^{2}x}=csc^{2}x\\ \frac{cos^{2}x}{sen^{2}x}+1=csc^{2}x \\cot^{2}x+1=csc^{2}x\\sabemos.que.cot^{2}x+1=csc^{2}x\\csc^{2}x=csc^{2}x$

$1-2 sen^{2}x= \frac{1- tan^{2}x }{1+ tan^{2}x } \\1-2 sen^{2}x= \frac{1- \frac{sen^{2}x}{cos^{2}x} }{1+ \frac{sen^{2}x}{cos^{2}x} } \\1-2 sen^{2}x= \frac{ \frac{cos^{2}x-sen^{2}x}{cos^{2}x} }{\frac{cos^{2}x+sen^{2}x}{cos^{2}x}} \\1-2 sen^{2}x= \frac{cos^{2}x-sen^{2}x}{cos^{2}x+sen^{2}x} \\sabemos.que.cos^{2}x+sen^{2}x=1\\1-2 sen^{2}x=cos^{2}x-sen^{2}x\\sabemos.que.cos^{2}x=1-sen^{2}x\\1-2 sen^{2}x=1- sen^{2}x-sen^{2}x\\1-2 sen^{2}x=1-2 sen^{2}x$


espero te sirva :)