Question

упростите выражение
(1-cos^альфа)tg^2альфа+1-tg^2альфа

Answer 1

$(1-cos^2alpha)tg^2alpha+1-tg^2alpha=sin^2alpha *tg^2alpha+1-tg^2alpha=\={sin^4alpha+sin^2alpha*cos^2alpha+cos^4alpha-sin^2alphaover cos^2alpha}={sin^4alpha+sin^2alpha*(-sin^2alpha)+cos^4alphaover cos^2alpha}=cos^2alpha$