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Mathematics

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

Trigonometric Identities

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Answer

sin x + cos y = 1

⇒ sin 30° + cos y = 1

⇒ $\dfrac{1}{2} + \text{cos y} = 1$

⇒ $\text{cos y} = 1 - \dfrac{1}{2}$

⇒ $\text{cos y} = \dfrac{1}{2}$

⇒ cos y = cos 60°

Hence, y = 60°.

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