Question

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

Options

• 0

• – 1

• `1/2`

• 1

Answer 1

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

Explanation:

cos(270^∘ + θ) ⋅ cos(90^∘ − θ) − sin(270^∘ − θ) ⋅ cos(θ)

Step-by-step using identities:

cos(270^∘ + θ) = −sin θ

cos(90^∘ − θ) = sin θ

sin(270^∘ − θ) = −cos θ

Substitute the values:

(−sin θ)(sin θ) − (−cos θ)(cos θ) = −sin² θ + cos² θ

cos² θ − sin² θ = cos(2θ)

So, the value depends on θ, and is not always 1.

But if θ = 0°:

cos(2 ⋅ 0^∘) = cos(0^∘) = 1