Prove that sin alpha * sin (90 - alpha) - cos (90-alpha) * cos alpha

Question

Mathematics

Matilda Gonzales

13 April, 06:50

Prove that sin alpha * sin (90 - alpha) - cos (90-alpha) * cos alpha

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Answers (1)

Know the Answer?

Kiley Costa · Answer 1

It is equal to 0.

Step-by-step 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.