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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