Question

If cos (α + β) = 0, then sin (α – β) can be reduced to ______.

Options

• cos β

• cos 2β

• sin α

• sin 2α

Answer 1

If cos (α + β) = 0, then sin (α – β) can be reduced to cos 2β.

Explanation:

According to the question,

cos(α + β) = 0

Since, cos 90° = 0

We can write,

cos(α + β) = cos 90°

By comparing cosine equation on L.H.S and R.H.S,

We get,

(α + β) = 90°

α = 90° – β

Now we need to reduce sin(α – β),

So, we take,

sin(α – β) = sin(90° – β – β) = sin(90° – 2β)

sin(90° – θ) = cos θ

So, sin(90° – 2β) = cos 2β

Therefore, sin(α – β) = cos 2β