Question

Cos105°-sin105° как расписать :((((((

Answer 1

Cos105⁰ - Sin105⁰ = Cos(60⁰ + 45⁰) - Sin(60⁰ + 45⁰) =

= Cos60⁰ * Cos45⁰ - Sin60⁰ * Sin45⁰ - Sin60⁰ * Cos45⁰ - Sin45⁰ * Cos60⁰ =

$=\frac{1}{2}*\frac{\sqrt{2} }{2}-\frac{\sqrt{3} }{2}*\frac{\sqrt{2} }{2}-\frac{\sqrt{3} }{2}*\frac{\sqrt{2} }{2}-\frac{\sqrt{2} }{2}*\frac{1}{2}=-2*\frac{\sqrt{6} }{4}=-\frac{\sqrt{6} }{2}$