Question

casec^(B+C÷2) - tan^A÷2=1
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Answer 1

Answer:

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

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