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Which expression completes the trigonometric identity? sec( Pi/2- theta)= a)-cos theta...

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connorcolin3 | Valedictorian

Posted May 30, 2013 at 11:32 AM via web

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Which expression completes the trigonometric identity?

sec( Pi/2- theta)=

a)-cos theta

b)Sec theta

c)Csc theta

D) Sin theta

Tagged with algebra trig, math

1 Answer | Add Yours

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llltkl | College Teacher | Valedictorian

Posted May 30, 2013 at 12:13 PM (Answer #1)

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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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