Ctg²x-cos²x-ctg²xcos²x

Предыдущий
вопрос Следующий
вопрос

To simplify the expression ctg²x - cos²x - ctg²x*cos²x, we can use the trigonometric identities:

Therefore:

ctg²x - cos²x - ctg²xcos²
= (1/tan(x))² - cos²(x) - (1/tan(x))(cos²(x)
= (1/tan²(x)) - cos²(x) - (cos²(x)/tan(x)
= (1/sin²(x)) - cos²(x) - (cos²(x)*(1-sin²(x))/sin(x)
= (1/sin²(x)) - cos²(x) - (cos²(x)/sin(x) - cos²(x)sin(x)
= (1/sin²(x)) - cos²(x) - (cos(x)sin(x) - cos²(x)sin(x)
= (1/sin²(x)) - cos²(x) - cos(x)sin(x)(1 - cos(x)
= (1/sin²(x)) - cos²(x) - cos(x)sin(x)sin(x
= (1/sin²(x)) - cos²(x) - cos(x)sin²(x
= (1/sin²(x)) - cos²(x) - cos(x)(1 - cos²(x)
= (1/sin²(x)) - cos²(x) - cos(x) - cos(x)cos²(x
= (1/sin²(x)) - cos²(x) - cos(x) - cos(x) + cos(x)sin²(x
= (1/sin²(x)) - cos²(x) - 2cos(x) + cos(x
= (1/sin²(x)) - cos²(x) - cos(x
= csc²(x) - cos²(x) - cos(x)

Therefore, ctg²x - cos²x - ctg²xcos²x simplifies to csc²(x) - cos²(x) - cos(x).