Question

sin(A-B)=1/2 and cos(A+4B)=0. find A and B​

Answer 1

Solution :-

→ sin(A - B) = 1/2

→ sin(A - B) = sin30°

comparing we get,

→ A - B = 30° ----------------- Equation (1).

Similarly,

→ cos(A+4B) = 0

→ cos(A+4B) = cos90°

comparing,

→ (A + 4B) = 90° ----------------- Equation (2).

Subtracting Equation (1) From Equation (2) Now,

→ (A + 4B) - (A - B) = 90 - 30

→ A - A + 4B + B = 60°

→ 5B = 60°

→ B = 12° (Ans).

Putting This Value in Equation (1) now,

→ A - 12° = 30°

→ A = 30 + 12

→ A = 42° (Ans).

Hence Value of A & B is 42° & 12° Respectively.

Answer 2

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