Question

Докажите тождество
ПРОЩУ ПОМОГИТЕЕ 1+ctg^2a+1/cos^2a=1/sin^2a*cos^2a

Answer 1

$1+ctg^2a+ dfrac{1}{cos^2a}= \ \ =1+ dfrac{cos^2a}{sin^2a}+ dfrac{1}{cos^2a}= \ \ = dfrac{sin^2acos^2a+cos^4a+sin^2a}{sin^2acos^2a}= \ \ = dfrac{cos^2a(sin^2a+cos^2a)+sin^2a}{sin^2acos^2a}= \ \ = dfrac{sin^2a+cos^2a}{sin^2acos^2a}= \ \ = dfrac{1}{sin^2acos^2a}$