Which expression completes the trigonometric identity? sec( Pi/2- theta)= a)-cos theta b)Sec theta c)Csc theta D) Sin theta

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Let OPM be a right angled triangle, right angled at M.

angle MOP= theta then, angle OPM=pi/2-theta.

 

For the referance angle theta, we have

sin theta= PM/OP  or,  cosec theta= OP/PM ..........(i)

For the referance angle pi/2-theta, we have

cos(pi/2-theta)=PM/OP  or, sec(pi/2-theta)=OP/PM...............(ii)

From (i) and (ii), we obtain:

cosec theta= sec(pi/2-theta) =OP/PM

Therefore, the expression that completes the trigonometric identity sec(pi/2-theta)= is option c) cosec or csc theta.

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