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.

For the triangle ABC, if B or C is an obtuseangle, then a = b cos C + c cos B according to the law of sines and the additionformula.

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 obtuseangle.

So, ∠A = 180° – (B + C)

⇒ sin A = sin (180° – (B + C))

⇒ sin A = sin (B + C) (since we know that sin(180° – θ) = sinθ)

triangleABC, if B or C is anobtuseangle, thena = b cos C + c cos Baccording to thelawofsinesand theadditionformula.## What is the law of sines states?

triangleABC withangles∠A, ∠B, and ∠C and withsidesa, b, and csinA/a = sinB/b = sinC/ca/sinA = b/sinB = c/sinC## Calculation:

obtuseangle.∠A = 180° – (B + C)additionformula,lawofsines,substituting,a = b cos C + c cos Bproved.lawofsineshere: