Question

докажите тождество sin² a (1+ctg² a )-cos² a= sin² a

Answer 1

$sin^2a\cdot (1+ctg^2a)-cos^2a=sin^2a\cdot \frac{1}{sin^2a}-cos^2a=1-cos^2a=sin^2a\\\\sin^2a=sin^2a\\\\\\\star \; \; 1+ctg^2a=\frac{1}{sin^2a}\; \; \star \\\\\star \; \; sin^2a+cos^2a=1\; \; \Rightarrow \; \; sin^2a=1-cos^2a\; \; \star$