Question

1-cot^2 x / 1+cot^2 x = 1-2cos^2x

how do I prove this ?

Answer 1

\[\frac{1-\cot^2(x)}{1+\cot^2(x)}=\frac{1-\frac{\cos^2(x)}{\sin^2(x)}}{1+\frac{\cos^2(x)}{\sin^2(x)}}\]
\[\frac{1-\frac{\cos^2(x)}{\sin^2(x)}}{1+\frac{\cos^2(x)}{\sin^2(x)}} \cdot \frac{\sin^2(x)}{\sin^2(x)}\]
\[\frac{\sin^2(x)-\cos^2(x)}{\sin^2(x)+\cos^2(x)}=\frac{\sin^2(x)-\cos^2(x)}{1}=\sin^2(x)-\cos^2(x)\]
\[(1-\cos^2(x))-\cos^2(x)=1-\cos^2(x)-\cos^2(x)=1-2\cos^2(x)\]

Answer 2

thank you so much

Answer 3

sin^2(x)/sin2^(x) why did you multiply this ?