If 2 cos (A + B) = 2 sin (A - B) = 1; find the values of A and B.

2 cos (A + B) = 1 ⇒ cos (A + B) = ⇒ cos (A + B) = cos 60° So, A + B = 60° ...............(1) 2 sin (A - B) = 1 ⇒ sin (A - B) = ⇒ sin (A - B) = sin 30° So, A - B = 30° ...............(2) Adding equation (1) and (2), we get (A + B) + (A - B) = 60° + 30° ⇒ A + B + A - B = 90° ⇒ 2A = 90° ⇒ A = ⇒ A = 45° From equation (2), A - B = 30° ⇒ 45° - B = 30° ⇒ B = 45° - 30° ⇒ B = 15° Hence, A = 45° and B = 15°.

Solve for x :
cos² 30° + sin² 2x = 1

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Solve for x :
sin² 60° + cos² (3x - 9°) = 1

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If 4 cos² x = 3 and x is an acute angle; find the value of :
(i) x
(ii) cos² x + cot² x
(iii) cos 3x
(iv) sin 2x

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Mathematics

If 2 cos (A + B) = 2 sin (A - B) = 1; find the values of A and B.

Trigonometric Identities

Related Questions

Solve for x :
cos² 30° + sin² 2x = 1

Solve for x :
sin² 60° + cos² (3x - 9°) = 1

If 4 cos² x = 3 and x is an acute angle; find the value of :
(i) x
(ii) cos² x + cot² x
(iii) cos 3x
(iv) sin 2x

Mathematics

If 2 cos (A + B) = 2 sin (A - B) = 1; find the values of A and B.

Trigonometric Identities

Related Questions

Solve for x :cos2 30° + sin2 2x = 1

Solve for x :sin2 60° + cos2 (3x - 9°) = 1

If 4 cos2 x = 3 and x is an acute angle; find the value of :(i) x(ii) cos2 x + cot2 x(iii) cos 3x(iv) sin 2x

Solve for x :
cos² 30° + sin² 2x = 1

Solve for x :
sin² 60° + cos² (3x - 9°) = 1

If 4 cos² x = 3 and x is an acute angle; find the value of :
(i) x
(ii) cos² x + cot² x
(iii) cos 3x
(iv) sin 2x