Question

If cos (A + B+ C) = 1÷2 ; sin( 2A + B+C) = 1 and tan (A+B- C÷2) = 1 then find the values
of A, B, C using trigonometric ratios of angles 0°, 30°, 45°, 60° and 90°​

Answer 1

Answer:

A=30,B=0,C=30°

Step-by-step explanation:

cos (A+B+C)=1/2

cos(A+B+C)=cos 60°

A+B+C=60°. eq1

sin(2A+B+C)=1

sin(2A+B+C)=sin 90°

2A+B+C=90°. eq2

tan(A+B-C/2)=1

tan(A+B-C/2)=tan 45°

A+B-C/2=45°. eq3

subtracting eq1 &eq2

A=30°

subtracting eq2 & eq3

A+C/2=45°

30+C/2=45°

C/2=15°

C=30°

substitute value of A&C in eq1

we get B=0