Question

Traingle ABC prove that cosec (a+b/2)=sec c/2

Answer 1

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

Answer 2

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