Question

please look at the image this is a homework problem I would appreciate help with!

Answer 1

ANSWER:

$\sin (t+2\pi)-\cos (t+4\pi)+\tan (t+\pi)=c$

STEP-BY-STEP EXPLANATION:

We have the following expression:

$\sin (t+2\pi)-\cos (t+4\pi)+\tan (t+\pi)$

Now, we apply the angle sum identities in each case, just like this:

$\begin{gathered} \sin (t+2\pi)=\sin t\cdot\sin 2\pi+\cos t\cdot\cos 2\pi \\ \cos (t+4\pi)=\cos t\cdot\cos 4\pi+\sin t\cdot\sin 4\pi \\ \tan (t+\pi)=\frac{\tan t+\tan\pi}{1+\tan t\cdot\tan\pi} \end{gathered}$

We replace by the equivalences of a, b and c, like this:

$\begin{gathered} \sin t\cdot\sin 2\pi+\cos t\cdot\cos 2\pi=a\cdot0+b\cdot1=b \\ \cos t\cdot\cos 4\pi+\sin t\cdot\sin 4\pi=b\cdot1+a\cdot0=b \\ \frac{\tan t+\tan\pi}{1+\tan t\cdot\tan\pi}=\frac{c+0}{1+c\cdot0}=\frac{c}{1}=c \\ \\ \text{ Replacing:} \\ b-b+c=c \end{gathered}$