Traingle ABC prove that cosec (a+b/2)=sec c/2
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Answered by
12
To Prove:
codec(A+B)/2 = sec(C/2)
Let A,B and C be the angles of the triangle ∆ABC
Angle Sum Property of Triangle,
A + B + C = 180
→A + B = 180 - C
Dividing both sides by 2
→(A+B)/2 = 90 - C/2
Multiplying both sides by cosecant function
→cosec(A+B)/2 = cosec[90-C/2]
From sec∅=cosec(90-∅)
→cosec(A+B)/2 = sec(C/2)
Hence,proved
Answered by
9
Step-by-step explanation:
Step-by-step explanation: for 2 marks
A+B+C=180 (angle sum property)
A+B=180-C
LHS=cosec(A+B)/2
=cosec(180-C)/2
=cosec 90-C/2
=sec C/2
HENCE PROVED
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