1) sin 750° = sin(360° + 390°) = sin(390°) = sin(390° - 360°) = sin 30° = 1/2ctg50° = 1/tan50° = 1/(sin50°/cos50°) = cos50°/sin50° = √3tg(-120°) = -tan120° = -sin120°/cos120° = -(√3 / 2) / (-1/2) = √3
Therefore, sin 750° + ctg50° + tg(-120°) = 1/2 + √3 + √3 = 1/2 + 2√3
2) tg -cos__ = tg x - cos yWhen x = 3π, y = πtg 3π - cos π = 0 - (-1) = 1
3) Simplify π ctg(π+α) cos(__+α) = π cot(π+α) cos(π+α)cot(π+α) = cotπ cotα - 1 = 0 * cotα - 1 = -1cos(π+α) = -cosαTherefore, the expression simplifies to -π cosα
Hope this helps. Let me know if you need further clarification.
1) sin 750° = sin(360° + 390°) = sin(390°) = sin(390° - 360°) = sin 30° = 1/2
ctg50° = 1/tan50° = 1/(sin50°/cos50°) = cos50°/sin50° = √3
tg(-120°) = -tan120° = -sin120°/cos120° = -(√3 / 2) / (-1/2) = √3
Therefore, sin 750° + ctg50° + tg(-120°) = 1/2 + √3 + √3 = 1/2 + 2√3
2) tg -cos__ = tg x - cos y
When x = 3π, y = π
tg 3π - cos π = 0 - (-1) = 1
3) Simplify π ctg(π+α) cos(__+α) = π cot(π+α) cos(π+α)
cot(π+α) = cotπ cotα - 1 = 0 * cotα - 1 = -1
cos(π+α) = -cosα
Therefore, the expression simplifies to -π cosα
Hope this helps. Let me know if you need further clarification.