Let's break this down step by step:
Using the unit circle, we know that cos(240°) = -1/2Therefore, cos(-2π/3) = -1/2.
Using the unit circle, we know that tan(-135°) = -1Therefore, tan(-3π/4) = -1.
Therefore, the final result is √3/2.
Let's break this down step by step:
Calculate cos(-2π/3)cos(-2π/3) = cos(-120°) = cos(240°)
Using the unit circle, we know that cos(240°) = -1/2
Calculate tan(-3π/4)Therefore, cos(-2π/3) = -1/2.
tan(-3π/4) = tan(-135°)
Using the unit circle, we know that tan(-135°) = -1
Finally, multiply the resultsTherefore, tan(-3π/4) = -1.
√3 cos(-2π/3) tan(-3π/4) = √3 (-1/2) (-1) = √3/2
Therefore, the final result is √3/2.