show that,t for any triangle abc, even if b or c is an obtuse angle, a = b cos c + c cos b. use the law of sines to deduce the “addition formula” sin (b + c) = sin b cos c + sin c cos b.

Question

show that,t for any triangle abc, even if b or c is an obtuse angle,  a = b cos c + c cos b. use the law of sines to deduce the 'addition  formula'  sin (b + c) = sin b cos c + sin c cos b.

ngocdiep · Answer

For the  triangle  ABC, if B or C is an  obtuse   angle , then  a = b cos C + c cos B   according to the  law  of  sines  and the  addition   formula .    What is the law of sines states?  For a  triangle  ABC with  angles  ∠A, ∠B, and ∠C and with  sides  a, b, and c  Thus, we can write,   sinA/a = sinB/b = sinC/c   or   a/sinA = b/sinB = c/sinC     Calculation:  It is given that in a ΔABC,  The ∠B or ∠C is an  obtuse   angle .   So,  ∠A = 180° - (B + C)   ⇒ sin A = sin (180° - (B + C))  ⇒ sin A = sin (B + C) (since we know that sin(180° - θ) = sinθ)  From the  addition   formula ,  sin (B + C) = sin B cos C + sin C cos B  ⇒ sin A = sin (B + C)  ⇒ sin A = sin B cos C + sin C cos B  From the  law   of   sines ,  a/sinA = b/sinB = c/sinC = K  ⇒ aK =sin A, bK = sin B, cK = sin C  On  substituting ,  ⇒ sin A = sin B cos C + sin C cos B  ⇒ aK = bK cos C + cK cos B  ⇒ K(a) = K(b cos C + c cos B)  ∴  a = b cos C + c cos B   Hence it is  proved .    Learn more about the  law   of   sines  here:  https://brainly.com/question/2807639  #SPJ1

What is the law of sines states?

Calculation:

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