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Mathematics

Find value of x, if :

sin x = sin 60° cos 30° - cos 60° sin 30°

Trigonometric Identities

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Answer

Solving,

⇒sin x=32×32−12×12⇒sin x=34−14⇒sin x=24⇒sin x=12⇒sin x=sin 30°⇒x=30°.\Rightarrow \text{sin x} = \dfrac{\sqrt{3}}{2} \times \dfrac{\sqrt{3}}{2} - \dfrac{1}{2} \times \dfrac{1}{2} \\[1em] \Rightarrow \text{sin x} = \dfrac{3}{4} - \dfrac{1}{4} \\[1em] \Rightarrow \text{sin x} = \dfrac{2}{4} \\[1em] \Rightarrow \text{sin x} = \dfrac{1}{2} \\[1em] \Rightarrow \text{sin x} = \text{sin 30°} \\[1em] \Rightarrow x = 30°.

Hence, x = 30°.

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