Question

if A,B,C are the angles of a triangle , prove that tan (B+C)/2=cot A/2​

Answer 1

Answer:

Let me help you for this question

We know that ABC is a triangle so,

=> A + B + C = 180 ( Angle Sum property )

=> B + C = 180 - A ( Just took A the other side)

Divide LHS and RHS by 2

=>   $\frac{B + C}{2} = \frac{180 - A}{2} = 90 - \frac{A}{2}$

Now apply tan on both sides,

=>  $tan(\frac{B + C}{2} ) = tan(90 - \frac{A}{2} )$

=> $tan(\frac{B + C}{2}) = cot \frac{A}{2}$ ( Because tan ( 90 - theta ) = cot theta)

Hence proved

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