Question

(1-sin^2 x)/(1-cos^2 x)+tg x*ctg x

Answer 1

Ты точно ничего ни забыл

Answer 2

To simplify the expression, let's work on each term separately:

Term 1: (1 - sin^2(x)) / (1 - cos^2(x)) Using the identity sin^2(x) + cos^2(x) = 1, we can rewrite the numerator and denominator: (1 - sin^2(x)) = cos^2(x) (1 - cos^2(x)) = sin^2(x) So, the expression becomes: cos^2(x) / sin^2(x) Using the identity cos^2(x) = 1 - sin^2(x): (1 - sin^2(x)) / sin^2(x) (1 / sin^2(x)) - 1

Term 2: tan(x) * cot(x) Using the identity cot(x) = 1 / tan(x): tan(x) * (1 / tan(x)) 1

Combining the simplified terms: (1 / sin^2(x)) - 1 + 1 1 / sin^2(x)

Therefore, the simplified expression is 1 / sin^2(x).