Question

if A , B , C are interior angles of Triangle ABC , prove sin B + C /2 . sec A/2 = 1​

Answer 1

Step-by-step explanation:

We have,

$\tt{sin \left( \dfrac{ B + C }{2} \right) \cdot \: sec \left( \dfrac{ A}{2} \right)}$

$\sf{ = sin \left( \dfrac{ \pi - A }{2} \right) \cdot \: sec \left( \dfrac{ A}{2} \right)}$

$\sf{ = sin \left( \dfrac{ \pi }{2} - \dfrac{A }{2}\right) \cdot \: sec \left( \dfrac{ A}{2} \right)}$

$\sf{ = cos \left(\dfrac{A }{2}\right) \cdot \: sec \left( \dfrac{ A}{2} \right)}$

$\sf{ = 1}$