[Cos70°- cos60°]÷[sin 70°- sin50°]= -√3
To simplify the given expression, we will use the trigonometric identities for cosine and sine of the sum and difference of two angles:
1. Cosine Difference Identity:
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
2. Sine Difference Identity:
sin(a - b) = sin(a)cos(b) - cos(a)sin(b)
Given expression: [cos(70°) - cos(60°)] / [sin(70°) - sin(50°)]
= [cos(70°)cos(60°) + sin(70°)sin(60°) - cos(60°)] / [sin(70°)cos(50°) - cos(70°)sin(50°)]
= [cos(70°)cos(60°) + sin(70°)sin(60°) - cos(60°)] / [cos(70°)sin(40°) - cos(70°)sin(50°)]
= [0.5 - 0.5(sqrt(3)/2)] / [0.5(sqrt(3)/2) - 0.5]
= [0.5 - 0.5(sqrt(3)/2)] / [0.5(sqrt(3)/2) - 0.5]
= [0.5 - 0.5(sqrt(3)/2)] / [0.5(sqrt(3)/2) - 0.5]
= [0.5 - 0.5(sqrt(3)/2)] / [0.5(sqrt(3)/2) - 0.5]
= [-0.5(sqrt(3)/2)] / [-0.5]
= √3
Therefore, the simplified expression is √3.