Question

Упростите sina* cosa* ctga -1

Answer 1

Решение
sinx * cosx * сtgx - 1 = (sinx*cosx*cosx)/sinx - 1 = cos²x - 1 = - sin²x

Answer 2

Solving the equation

To solve the equation sin(a)*cos(a)*tg(a) - 1, let's break it down step-by-step:

1. Use trigonometric identities to simplify the terms: - sin(a)*cos(a) = (1/2)sin(2a) [[source 9]] - tg(a) = sin(a)/cos(a) 2. Substitute the identities: - (1/2)sin(2a)*sin(a)/cos(a) - 1 3. Simplify: - (1/2)sin(2a)tg(a) - 1

Solving for a

To solve for a, we set the equation equal to 0 and use trigonometric identities:

(1/2)sin(2a)tg(a) - 1 = 0 1/2*sin(2a)*tg(a) = 1 sin(2a) = 2 2a = sin^-1(2) a = (1/2)sin^-1(2)

Therefore, the simplified solution for a is a = (1/2)sin^-1(2).