The value of [tex]\tan \left(\frac{5\pi }{4}\right)[/tex] is 1
Explanation:
Given that the expression is [tex]\tan \left(\frac{5\pi }{4}\right)[/tex]
We need to determine the solution of the expression.
Let us rewrite the angles for the expression [tex]\tan \left(\frac{5\pi }{4}\right)[/tex]
Thus, we have,
[tex]\tan \left(\frac{5\pi }{4}\right)=\tan \left(\frac{4+1}{4}\pi \right)[/tex]
Simplifying, we get,
[tex]\tan \left(\frac{5\pi }{4}\right)=\tan \left(\left(\frac{4}{4}+\frac{1}{4}\right)\pi \right)[/tex]
Multiplying by π, we have,
[tex]\tan \left(\frac{5\pi }{4}\right)=\tan \left(\left\pi+\frac{1}{4}\right\pi \right)[/tex]
Since, we know that [tex]\tan \left(x+\pi \cdot \:k\right)=\tan \left(x\right)[/tex]
Applying the above rule, we have,
[tex]\tan \left(\pi +\frac{1}{4}\pi \right)=\tan \left(\frac{1}{4}\pi \right)[/tex]
Hence, simplifying, we have,
[tex]\tan \left(\frac{\pi }{4}\right)[/tex]
The value of [tex]\tan \left(\frac{\pi }{4}\right)[/tex] is 1
Thus, the value of the expression [tex]\tan \left(\frac{5\pi }{4}\right)[/tex] is 1
