Question

Find A and B if cos(2A-B)=sin(A+2B)=root3/2

Answer 1

Cos (2A - B) = sin (A + 2B) = √3 /2  = sin 60° = cos 30° = sin 120° = cos(330°)

2 A - B = 30°      ---------(1)
   or,    2 A  - B  = 330°   -----(2)

A +2 B = 60°    ----- (3)
   or,   A  + 2 B = 120    --- (4)

By using the 4 combinations of two equations we get:

  A = 24° and   B = 18°
or   A = 0°   and B = 30°

or    A = 144°   and B = -42° ie., 318°
or    A  = 12°  and    B = 54°

All these four combinations work correct,...

Answer 2

Answer:

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