1.
cos(90-x) = sin(x)
sin(-x) = -sin(x)
cos²(180+x) = (-cos²x) = cos²(x)
Then
cos(90-x) .sin(-x)/cos²(180+x) = sin(x).(-sin(x))/cos²(x)
= -sin²(x))/cos²(x)
= −tan²(x)
2.
tan² (360° + θ)/cos(90° + θ).sin(180° - θ)
tan² (360° + θ) = tan² (θ)
cos(90° +x) = - sin(θ)
sin(180° - θ) = sin(θ)
tan² (360° + θ)/cos(90° +θ).sin(180° - θ) = tan² (θ)/- sin(θ) sin(θ)
= -tan²(θ)/sin²(θ)
= -1/cos²(θ)
= - (cos²θ + sin²θ)/cos²θ
= -1 - tan²θ
