Question

Помогите с тремя заданиями,пожалуйста

Answer 1

$2sin^2(45^circ-3t)+sin6t=1-cos2(45^circ-3t)+sin6t=\=1-cos(90^circ-6t)+sin 6t=1-sin6t+sin6t=1$

$sin84^circ+cos234^circ-sin24^circ=sin(90^circ-6^circ)+cos(270^circ-36^circ)-\-sin24^circ=cos6^circ-sin36^circ-sin24^circ=cos6^circ-2sinfrac{36^circ+24^circ}{2}cosfrac{36^circ-24^circ}{2}\=cos6^circ-2sin30^circcos6^circ=cos6^circ-cos6^circ=0$

$sin x-sqrt3cos x=1\ frac12sin x-frac{sqrt3}2cos x=frac12\ sin xcos60^circ-cos xsin 60^circ=frac12\ sin(x-60^circ)=frac12\ x-60^circ=(-1)^kcdot 30^circ+180^circ k,quad kinmathbb Z\ x=60^circ+(-1)^kcdot 30^circ+180^circ k,quad k in mathbb Z$