Question

[Bình Trần Thị]

cho tam giác ABC , chứng minh rằng : a) sin(B + C) = sinA    ;   b) cos(A + B) = -cosC   ;   c) sin\(\frac{B+C}{2}\) = cos\(\frac{A}{2}\)    ;   d) tan\(\frac{A+C}{2}\) = cot\(\frac{B}{2}\) 

Answer 1

[Silverbullet]

a) Sin (B+C) = Sin (180-A) = Sin A
b) Cos (A+B) = Cos ( 180-A) = Cos A
c) Sin (\(\dfrac{B+C}{2}\)) = Sin \(\left(\dfrac{180-A}{2}\right)\)= Sin \(\left(90^0-\dfrac{A}{2}\right)\)= Cos \(\dfrac{A}{2}\)

d) Tan \(\left(\dfrac{A+C}{2}\right)\)= Tan\(\left(\dfrac{180-B}{2}\right)\)=Tan\(\left(90^0-\dfrac{B}{2}\right)\)= Cot \(\dfrac{B}{2}\)