Question

Find acute angles A, B and C, if sin (A+B – C) = 1 2 and cos (B + C – A) = 1 2 and tan (C + A– B) = 1 , A>B.​

Answer 1

Answer:

(π/8,3π/8,π/4)

sin(B+C−A)=1

⇒B+C−A=

2

π

....(eq1)

cos(C+A−B)=1

⇒C+A−B=0....(eq2)

tan(A+B−C)=1

⇒A+B−C=

4

π

....(eq3)

adding (eq1) and (eq2) we get

2C=

2

π

C=

4

π

adding (eq2)and (eq3) we get

2A=

4

π

A=

8

π

adding (eq1)and (eq3) we get

2B=

2

π

+

4

π

2B=

4

3π

B=

8

3π

Step-by-step explanation:

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