(sin(pi/4-a)+cos(pi/4-a))/(sin(pi/4-a)-cos(pi/4-a)) упростить

Предыдущий
вопрос Следующий
вопрос

To simplify the given expression, we can first simplify the numerator and denominator separately.

Numerator
sin(pi/4 - a) + cos(pi/4 - a
Using the angle subtraction formula for sine and cosine
sin(pi/4)cos(a) - cos(pi/4)sin(a) + cos(pi/4)cos(a) + sin(pi/4)sin(a
= sqrt(2)/2 cos(a) - sqrt(2)/2 sin(a) + sqrt(2)/2 cos(a) + sqrt(2)/2 sin(a
= sqrt(2) * cos(a)

Denominator
sin(pi/4 - a) - cos(pi/4 - a
Using the angle subtraction formula for sine and cosine
sin(pi/4)cos(a) - cos(pi/4)sin(a) - cos(pi/4)cos(a) - sin(pi/4)sin(a
= sqrt(2)/2 cos(a) - sqrt(2)/2 sin(a) - sqrt(2)/2 cos(a) - sqrt(2)/2 sin(a
= -sqrt(2) * sin(a)

Therefore, the simplified expression is
(sqrt(2) cos(a)) / (-sqrt(2) sin(a)
= -cot(a)