Question

Cos105°-sin105° как расписать :((((((

Answer 1

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

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

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