Question

find the exact value of cos (2 theta - pi over 2)

Answer 1

One rule we need to know is: \(cos (-\theta) = cos\theta \)

You are given: \[cos (2\theta - \frac{\pi}{2})\]
Take the minus sign common:
You'll get;
\[cos (-(-2\theta + \frac{\pi}{2})) = cos (\frac{\pi}{2}-2\theta)\]

cos (90-a) = sin a

Thus, \[cos (\frac{\pi}{2}-2\theta) = sin 2\theta\]

Understood? :)