Question
Prove that each equation is an identity.$$\cos \left(t+\frac{\pi}{4}\right)=(\cos t-\sin t) / \sqrt{2}$$
Step 1
The formula is $\cos(a+b) = \cos a \cos b - \sin a \sin b$. Here, $a=t$ and $b=\frac{\pi}{4}$. So, we get: $$\cos \left(t+\frac{\pi}{4}\right) = \cos t \cos \frac{\pi}{4} - \sin t \sin \frac{\pi}{4}.$$ Show more…
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