Question

Which of the following is not equal to sec⁡(-85°)?

sec⁡(85°)
-sec⁡(-95°)
sec⁡(275°)
sec⁡(-95°)

Answer 1

-85 degrees in is the 4th quadrant so the cos and sec will be positive
sec is also positive in first quadrant so sec(85) will be equal to sec(-85)
Sec is is negative in 3rd quadrant so -sec(-95) will be same also.

sec 275 is in 3rd quadrant so will be negative so not equal
also sec(-95) will be same angle as sec 275

the last 2 options are not equal to sec(-85)

Answer 2

Answer: The correct option is (D)
`\sec(-95^\circ).`

Step-by-step explanation: We are given to select the correct option that is not equal to
`\sec(-85^\circ).`

Option (A) :
`\sec(85^\circ).`

Since secant of any angle is an even function, so

`\sec(-\theta)=\sec\theta.`

Therefore,

`\sec(-85^\circ)=\sec85^\circ.`

So, this option is not correct.

Option (B) :
`-\sec(-95^\circ).`

We have

`-\sec(-95^\circ)=-\sec95^\circ=-sec(2*90^\circ-85^\circ)=-(-\sec85^\circ)=\sec85^\circ=\sec(-85^\circ).`

So, this option is also not correct.

Option (C) :
`\sec(275^\circ).`

We have

`\sec275^\circ=\sec(4*90^\circ-85^\circ)=\sec85^\circ= \sec(-85^\circ).`

So, this option is incorrect.

Option (D) :
`\sec(-95^\circ).`

We have

`\sec(-95^\circ)=\sec95^\circ=\sec(2*90^\circ-85^\circ)=-\sec85^\circ\\eq \sec(-85^\circ).`

So, this option is correct.

Thus, (D) is the correct option.