Question

Prove that sin alpha × sin(90- alpha) - cos(90-alpha) × cos alpha​

Answer 1

It is equal to 0.

Explanation:

I can simplify it as follows:

sinα sin(90 - α) - cos(90 - α)(cosα)

Now sin(90 -α) = cosα and cos(90 - α) = sinα) ( for α < 90)

So the expression becomes:

sinαcosα - sinαcosα

= 0 .