Given:
[tex]\text{tan}(t)=\frac{5}{7}[/tex]
To find:
Value of [tex]\text{tan}(t-\pi )[/tex]
Solution:
To solve the given expression we will use the identity,
[tex]\text{tan}(A-B)=\frac{\text{tan}A-\text{tan}B}{1+\text{tan}A\text{tan}B}[/tex]
Now substitute the values,
[tex]A=t[/tex]
[tex]B=\pi[/tex]
[tex]\text{tan}(t-\pi)=\frac{\text{tan}t-\text{tan}\pi }{1+\text{tan}t\text{tan}\pi }[/tex]
Since, the value of [tex]\text{tan}(\pi )[/tex] is [tex]0[/tex].
[tex]\text{tan}(t-\pi)=\frac{\text{tan}t-0}{1+\text{tan}t\times (0)}[/tex]
[tex]=\frac{\text{tan}t}{1}[/tex]
[tex]=\text{tan}t[/tex]
Therefore, [tex]\text{tan}(t-\pi)=\frac{5}{7}[/tex] will be the answer.
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