Question

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

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

$-\sec(-95^\circ)=-\sec95^\circ=-sec(2\times90^\circ-85^\circ)=-(-\sec85^\circ)=\sec85^\circ=\sec(-85^\circ).$

So, this option is also not correct.

Option (C) :  $\sec(275^\circ).$

We have

$\sec275^\circ=\sec(4\times90^\circ-85^\circ)=\sec85^\circ= \sec(-85^\circ).$

So, this option is incorrect.

Option (D) :  $\sec(-95^\circ).$

We have

$\sec(-95^\circ)=\sec95^\circ=\sec(2\times90^\circ-85^\circ)=-\sec85^\circ\neq \sec(-85^\circ).$

So, this option is correct.

Thus, (D) is the correct option.