Question

HELP ASAP Find the exact value of sin15° by using a sum or difference formula. BRANLIEST ​

Answer 1

The exact value of sin 15° is $\frac{\sqrt{3}-1}{2\sqrt{2}}$.

Solution:

45 – 30 = 15

sin 15° can be written as sin (45° – 30°).

Using trigonometric difference formula:

sin(A – B) = sin A cos B – cos A sin B

sin (45° – 30°) = sin 45° cos 30° – cos 45° sin 30°

The value of sin 45° = $\frac{1}{\sqrt{2}}$

The value of cos 30° = $\frac{\sqrt{3}}{2}$

The value of cos 45° = $\frac{1}{\sqrt{2}}$

The value of sin 30° = $\frac{1}{2}$

Substitute these values, we get  

$\sin \left(45^{\circ}-30^{\circ}\right)=\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{3}}{2}-\frac{1}{\sqrt{2}} \cdot \frac{1}{2}$

                       $=\frac{\sqrt{3}}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}$

                       $=\frac{\sqrt{3}-1}{2\sqrt{2}}$

$\sin \left(45^{\circ}-30^{\circ}\right)=\frac{\sqrt{3}-1}{2\sqrt{2}}$

$\sin15^\circ}=\frac{\sqrt{3}-1}{2\sqrt{2}}$

Hence the exact value of sin 15° is $\frac{\sqrt{3}-1}{2\sqrt{2}}$.

Answer 2

Answer:

$\frac{\sqrt{6}-\sqrt{2} }{4}$

Step-by-step explanation: