If sin(A + B) = √3/2 = cos(A - B), 0° B), find the values of A and B.

Given, ⇒ sin(A + B) = ⇒ sin(A + B) = sin 60° ⇒ A + B = 60° ..........(1) Also, ⇒ cos(A - B) = ⇒ cos(A - B) = cos 30° ⇒ A - B = 30° ..........(2) Adding, (1) and (2), we get : ⇒ (A + B) + (A - B) = 60° + 30° ⇒ A + A + B - B = 90° ⇒ 2A = 90° ⇒ A = 45°. Substituting value of A in (1), we get : ⇒ A + B = 60° ⇒ 45° + B = 60° ⇒ B = 60° - 45° ⇒ B = 15°. Hence, A = 45° and B = 15°.

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Mathematics

If sin(A + B) = √3/2 = cos(A - B), 0° < A + B ≤ 90° (A > B), find the values of A and B.

Trigonometrical Ratios

Related Questions

In the right-angled triangle ABC, ∠C = 90° and ∠B = 60°. If AC = 6 cm, find the lengths of the sides BC and AB.

If 3 tan² θ - 1 = 0, find cos 2θ, given that θ is acute.

If the length of each side of a rhombus is 8 cm and its one angle is 60°, then find the lengths of the diagonals of the rhombus.

If sin x + cos y = 1, x = 30° and y is acute angle, find the value of y.

Mathematics

If sin(A + B) = √3/2 = cos(A - B), 0° < A + B ≤ 90° (A > B), find the values of A and B.

Trigonometrical Ratios

Related Questions

In the right-angled triangle ABC, ∠C = 90° and ∠B = 60°. If AC = 6 cm, find the lengths of the sides BC and AB.

If 3 tan2 θ - 1 = 0, find cos 2θ, given that θ is acute.

If the length of each side of a rhombus is 8 cm and its one angle is 60°, then find the lengths of the diagonals of the rhombus.

If sin x + cos y = 1, x = 30° and y is acute angle, find the value of y.

If 3 tan² θ - 1 = 0, find cos 2θ, given that θ is acute.