Question

find the value cos 105° step by step​

Answer 1

Step-by-step explanation:

Using the identity of cos(A+B)

we can find the value of cos 105°

Cos (A+B) = CosACosB -SinAsinB

cos(60°+45°) = cos60°cos45° - sin60°sin45°

=

$= \frac{1}{2} ( \frac{1}{ \sqrt{2} }) - \frac{ \sqrt{3} }{2} ( \frac{1}{ \sqrt{2} } ) \\ \\ = \frac{1}{ 2\sqrt{2} } - \frac{ \sqrt{3} }{2 \sqrt{2} } \\ \\ = \frac{1 - \sqrt{3} }{2 \sqrt{2} } \\ \\ hope \: this \: helps \: you$