Tg150°*sin200°/cos320°*ctg140°

Предыдущий
вопрос Следующий
вопрос

To simplify the given expression, we need to first convert all the trigonometric functions to their corresponding functions involving sine and cosine.

Convert ctg(140°) to cos(140°)/sin(140°)

Then we have
Tg(150°) Sin(200°) / Cos(320°) (Cos(140°) / Sin(140°))

Now we can simplify by cancelling out the like terms:

= tan(150°) sin(200°) / cos(320°) (cos(140°) / sin(140°)
= tan(150°) sin(200°) cos(140°) / cos(320°) * sin(140°)

Now we can simplify further by using trigonometric identities:

= (tan(150°) = - cot(30°) = -tan(120°))

= -tan(120°) sin(200°) cos(140°) / cos(320°) * sin(140°)

= -tan(120°) sin(200°) cos(140°) / cos(320°) * sin(140°)

Since tan(120°) = -√
= -√3 sin(200°) cos(140°) / cos(320°) * sin(140°)

Therefore, the simplified expression is -√3 sin(200°) cos(140°) / cos(320°) * sin(140°)