Question

How do you use the sum or difference identity to find the excat value of sin 165°​

Answer 1

Answer:

$\frac{1}{4}$ ($\sqrt{6}$ - $\sqrt{2}$ )

Step-by-step explanation:

Using the addition formula for sine

sin(A + B) = sinAcosB + cosAsinB

Given

sin165° = sin(120 + 45)° , then

sin(120 + 45)°

= sin120°cos45° + cos120°sin45°

= sin60°cos45°  - cos60°sin45°

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

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

= $\frac{1}{4}$ ( $\sqrt{6}$ - $\sqrt{2}$ )