Let's simplify each term separately:
sin^2(-π/3):Recall that sin(-θ) = -sin(θ) for all angles θ. Therefore, sin^2(-π/3) = (-sin(π/3))^2 = (-√3/2)^2 = 3/4.
cos^2(-π/6):Similarly, cos(-θ) = cos(θ) for all angles θ. So, cos^2(-π/6) = (cos(π/6))^2 = (√3/2)^2 = 3/4.
Finally, adding both terms together yields:sin^2(-π/3) + cos^2(-π/6) = 3/4 + 3/4 = 6/4 = 3/2.
Therefore, sin^2(-π/3) + cos^2(-π/6) = 3/2.
Let's simplify each term separately:
sin^2(-π/3):
Recall that sin(-θ) = -sin(θ) for all angles θ. Therefore, sin^2(-π/3) = (-sin(π/3))^2 = (-√3/2)^2 = 3/4.
cos^2(-π/6):
Similarly, cos(-θ) = cos(θ) for all angles θ. So, cos^2(-π/6) = (cos(π/6))^2 = (√3/2)^2 = 3/4.
Finally, adding both terms together yields:
sin^2(-π/3) + cos^2(-π/6) = 3/4 + 3/4 = 6/4 = 3/2.
Therefore, sin^2(-π/3) + cos^2(-π/6) = 3/2.