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If A,B and C are interior of a triangle ABC Show that, cosec 2 (B+C /2)-tan 2 A/2=1

If A,B and C are interior of a triangle ABC Show that,
cosec2(B+C/2)-tan2A/2=1
 

Grade:10

1 Answers

Arun
25750 Points
6 years ago
Dear Varsha
 
As we know
Cosec (90 - theta) = sec theta
 
Now
A+ B +C = 180°
Hence
B+C/2 = 90 - (A/2)
 
Now
 
Cosec²(90- A/2)  - tan²A/2
sec²A/2 - tan²A/2
= 1
= RHS
 
Hence proved
 
 
Regards
Arun (askIITians forum expert)

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