Question

Cosec2(b+c/2)-tan2(a/2)=1

Answer 1

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Answer 2

In a Δ
sum of all angles=180°
a+b+c=180
    b+c=180-a                                .................1
then in given statement taking LHS
       =cosec²(b+c/2)-tan²(a/2)
 substituting 1 in cosec²(b+c/2)
       =cosec²(180/2-a/2)-tan²(a/2)
       =cosec²(90-a/2)-tan²(a/2)
       (identity  cosec(90-Ф)=secФ)
then =sec²(a/2)-tan²(a/2)
       (identity sec²Ф-tan²Ф=1)
  so  =1 ⇒ RHS 
                                                                                   HENCE PROVED

:) Hope this helps!!!!!!!!!!