If tan(−
4
7π
)=x, then the value of x is:
- A-1/2
- B−
3
/2 - C3
/2 - D1
Solution & Step-by-step Explanation
We know that tan(−θ)=−tanθ. Therefore:
tan(−
4
7π
)=−tan(
4
7π
)
Now, express
4
7π
in terms of 2π:
4
7π
=2π−
4
π
Since tan(2π−θ)=−tanθ:
tan(
4
7π
)=tan(2π−
4
π
)=−tan(
4
π
)=−1
Substitute this back into the original relation:
x=−tan(
4
7π
)=−(−1)=1
tan(−
4
7π
)=−tan(
4
7π
)
Now, express
4
7π
in terms of 2π:
4
7π
=2π−
4
π
Since tan(2π−θ)=−tanθ:
tan(
4
7π
)=tan(2π−
4
π
)=−tan(
4
π
)=−1
Substitute this back into the original relation:
x=−tan(
4
7π
)=−(−1)=1