Verified Answer :

welshfella

-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:  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

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

So, this option is correct.

Thus, (D) is the correct option.

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