(cos^2t - ctg^2t)/(sin^2t - tg^2t)

Предыдущий
вопрос Следующий
вопрос

To simplify the expression (cos^2t - cot^2t)/(sin^2t - tan^2t), we can first rewrite cot^2t as 1/tan^2t and cot^2t as 1/sin^2t:

= (cos^2t - 1/tan^2t)/(sin^2t - 1/sin^2t)

Now, we can combine the terms over a common denominator:

= [(cos^2t sin^2t - 1)/(sin^2t tan^2t)] / [(sin^2t sin^2t - 1)/(sin^2t sin^2t)]

= [(cos^2t sin^2t - 1)/(sin^2t tan^2t)] [(sin^2t sin^2t)/(sin^2t * sin^2t - 1)]

= [(sin^2t cos^2t - 1)/(tan^2t)] [1/(sin^2t - 1/sin^2t)]

= [sin^2t cos^2t - 1]/[tan^2t (sin^2t - 1/sin^2t)]

This is the simplified expression.