Cosx/1-sinx - cosx/1+since

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вопрос

To simplify the expression, we can find a common denominator for the two fractions:

cos(x)/(1-sin(x)) - cos(x)/(1+sin(x))

To find a common denominator, we multiply the first fraction by (1+sin(x))/(1+sin(x)) and the second fraction by (1-sin(x))/(1-sin(x)):

[cos(x)(1+sin(x))] / [(1-sin(x))(1+sin(x))] - [cos(x)(1-sin(x))] / [(1-sin(x))(1+sin(x))]

Expanding the numerators:

[cos(x) + cos(x)sin(x)] / (1-sin^2(x)) - [cos(x) - cos(x)sin(x)] / (1-sin^2(x))

Simplifying further:

[cos(x) + cos(x)sin(x) - cos(x) + cos(x)sin(x)] / (1-sin^2(x))

[2cos(x)] / cos^2(x)

2cos(x)