Question

sin (270° – θ) sin (90° – θ) – cos ( 270° – θ) cos (90° + θ) is ______.

Options

• 0

• 1

• –1

• 2

Answer 1

sin (270° – θ) sin (90° – θ) – cos ( 270° – θ) cos (90° + θ) is –1.

Explanation:

We have,

sin (270° – θ) sin (90° – θ) – cos ( 270° – θ) cos (90° + θ) 

= – cos θ . cos θ – (– sin θ) (– sin θ)

= – cos² θ – sin² θ

= – (cos² θ + sin² θ)

= –1   ...[∵ sin² θ + cos² θ = 1]