Question

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

Answer 1

Ответ:

2cos a / 1

Пошаговое объяснение:

(cos a / 1 - sin a) + (cos a / 1 + sin a) = cos a / 1 - sin a + cos a / 1 + sin a = 2cos a/1(синусы сокращаются).

Answer 2

The expression can be simplified using a common denominator:

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

To find the common denominator, we multiply the denominators together:

[(cos a * (1 + sin a)) + (cos a * (1 - sin a))] / [(1 - sin a) * (1 + sin a)]

Simplifying further:

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

Combining like terms:

[2cos a] / (1 - sin^2 a)

Using the identity sin^2 a + cos^2 a = 1:

[2cos a] / cos^2 a

Simplifying:

2 / cos a

Therefore, the simplified expression is 2 / cos a.