Question

In a ABC, if sin A - cos B = cos C,
then what is B equal to?​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Answer: (1) π/2

Explanation :

In a triangle ABC,

A + B + C = π….(i)

Given,

sin A – cos B = cos C

sin A = cos B + cos C

Using the formulas sin 2x = 2 sin x cos x and cos x + cos y = 2 cos(x + y)/2 cos(x – y)/2,

2 sin A/2 cos A/2 = 2 cos(B + C)/2 cos(B – C)/2

sin A/2 cos A/2 = cos(π – A)/2 cos(B – C)/2 {from (i)}

sin A/2 cos A/2 = cos[π/2 – A/2] cos(B – C)/2

sin A/2 cos A/2 = sin A/2 cos(B – C)/2

cos A/2 = cos(B – C)/2

Thus, A/2 = (B – C)/2

A = B – C….(ii)

From (i) and (ii),

2B = π

Therefore, ∠B = π/2