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Using the formula, sin(A – B) = sinA cosB – cosA sinB, find the value of sin 15º - Mathematics

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Sum

Using the formula, sin(A – B) = sinA cosB – cosA sinB, find the value of sin 15º

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Solution

Let A = 45º and B = 30º. Then A – B = 15º.

Putting A = 45º and B = 30º in the given formula, we get

sin(45º – 30º) = sin45º cos30º – cos45º sin30º

or, `\sin (45^\text{o}-30^\text{o})=\frac{1}{\sqrt{2}}\times\frac{\sqrt{3}}{2}-\frac{1}{\sqrt{2}}\times \frac{1}{2} `

`=\frac{\sqrt{3}-1}{2\sqrt{2}}\Rightarrow \sin15^\text{o}=\frac{\sqrt{3}-1}{2\sqrt{2}}`

Concept: Trigonometric Ratios of Some Special Angles
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