tan 3pi/4 is equal to -1
Solution:
Given that we have to find value of [tex]\tan \frac{3 \pi}{4}[/tex]
Let us evaluate the given expression
[tex]\tan \frac{3 \pi}{4}=\tan \left(\pi-\frac{\pi}{4}\right)[/tex]
[tex]\tan (a-b)=\frac{\tan a-\tan b}{1+\tan a \tan b}[/tex] ---- eqn 1
[tex]\text{In} \tan \left(\pi-\frac{\pi}{4}\right), a=\pi \text { and } b=\frac{\pi}{4}[/tex]
Substituting the values in eqn 1,
[tex]\tan \left(\pi-\frac{\pi}{4}\right)=\frac{\tan \pi-\tan \frac{\pi}{4}}{1+\tan \pi \tan \frac{\pi}{4}}[/tex]
we know that by trignometric values,
[tex]\tan \pi=0 \text { and } \tan \frac{\pi}{4}=1[/tex]
Substituting these values we get,
[tex]\tan \left(\pi-\frac{\pi}{4}\right)=\frac{0-1}{1+0(1)}=\frac{-1}{1}=-1[/tex]
Therefore,
[tex]\tan \left(\pi-\frac{\pi}{4}\right)=\tan \frac{3 \pi}{4}=-1[/tex]
Thus the value of tan 3pi/4 is -1
