(Cos70-cos50)÷(sin70-sin50) =-√3
Let's simplify the expression step by step:
(cos70 - cos50) / (sin70 - sin50)
Using the trigonometric identity cos(a) - cos(b) = -2sin((a+b)/2)sin((a-b)/2), we get:
(cos70 - cos50) = -2sin(60)sin(10) = -2(√3/2)(sin10) = -√3sin10
Similarly, using the trigonometric identity sin(a) - sin(b) = 2cos((a+b)/2)sin((a-b)/2), we get:
(sin70 - sin50) = 2cos(60)sin(10) = 2(1/2)sin(10) = sin(10)
Therefore, the expression becomes:
(-√3sin10) / sin10 = -√3
So, the value of the expression is -√3.