If sec(−
4
5π
)=x, then the value of x is:
- A−
2
1
- B−
2
- C−1
- D2
Solution & Step-by-step Explanation
Given expression: x=sec(−
4
5π
)
Using the identity sec(−θ)=secθ:
x=sec(
4
5π
)
Now, rewrite
4
5π
as π+
4
π
:
x=sec(π+
4
π
)
Since sec(π+θ)=−secθ (as it lies in the third quadrant where secant is negative):
x=−sec(
4
π
)
We know that sec(
4
π
)=
2
, therefore:
x=−
2
(Note: The options provided in the raw text contain formatting artifacts representing −
2
as −2 with layout lines. The correct value is −
2
)
4
5π
)
Using the identity sec(−θ)=secθ:
x=sec(
4
5π
)
Now, rewrite
4
5π
as π+
4
π
:
x=sec(π+
4
π
)
Since sec(π+θ)=−secθ (as it lies in the third quadrant where secant is negative):
x=−sec(
4
π
)
We know that sec(
4
π
)=
2
, therefore:
x=−
2
(Note: The options provided in the raw text contain formatting artifacts representing −
2
as −2 with layout lines. The correct value is −
2
)