Example
If α=30°\alpha = 30\degreeα=30° and β=45°\beta= 45\degreeβ=45° sin(30°+45°)=sin30° cos45°+sin45° cos30°==12⋅22+22⋅32=2+64\sin(30\degree+45\degree)=\sin30\degree \, \cos45\degree + \sin45\degree \, \cos30\degree =\\= \dfrac{1}{2}\cdot\dfrac{\sqrt{2}}{2}+\dfrac{\sqrt{2}}{2}\cdot \dfrac{\sqrt{3}}{2}=\dfrac{\sqrt{2}+\sqrt{6}}{4}sin(30°+45°)=sin30°cos45°+sin45°cos30°==21⋅22+22⋅23=42+6
Description
This formula shows how to factor the sum of two fifth powers.
Example 1:| (a−2)2=a2−2⋅a⋅2+22=a2−4a+4(a-2)^2 = a^2 - 2\cdot a \cdot 2 + 2^2 = a^2 - 4a + 4(a−2)2=a2−2⋅a⋅2+22=a2−4a+4 Example 2:| A (3x-5y)^2 &= (3x)^2 - 2 \cdot 3x \cdot 5y + (5y)^2\\ &= 9x^2 - 30xy + 25y^2 A