Выполни задание

Для любого острого угла \(\alpha\) справедливы равенства \(\sin (90\degree-\alpha)=\cos \alpha\) , \(\cos (90\degree-\alpha)=\sin \alpha\) .

\(\sin (90\degree-\alpha)=\dfrac{AC}{AB}=\cos \alpha\) ,

\(\cos (90\degree-\alpha)=\dfrac{BC}{AB}=\sin \alpha\) .

Функция	Угол \(30\degree\)	Угол \(45\degree\)	Угол \(60\degree\)
\(\sin\)	\(\dfrac{1}{2}\)	\(\dfrac{\sqrt{2}}{2}\)	\(\dfrac{\sqrt{3}}{2}\)
\(\cos\)	\(\dfrac{\sqrt{3}}{2}\)	\(\dfrac{\sqrt{2}}{2}\)	\(\dfrac{1}{2}\)
\(\tg\)	\(\dfrac{\sqrt{3}}{3}\)	\(1\)	\(\sqrt{3}\)
\(\ctg\)	\(\sqrt{3}\)	\(1\)	\(\dfrac{\sqrt{3}}{3}\)

Вычисли значения выражений:

1. \(\sin 45\degree-\cos 45\degree+\tg 45\degree\) ;

2. \(\sin 30\degree+\cos 60\degree-1\) ;

3. \(\sin 60\degree\cdot \cos 30\degree+\dfrac{1}{4}\) ;

4. \(4\sin 30\degree\cdot \cos 60\degree-\ctg 45\degree\) ;

5. \(2\tg 30\degree\cdot \tg 60\degree+4{(\sin 60\degree)}^2\) ;

6. \(2\ctg 30\degree\cdot \ctg 60\degree+4{(\cos 30\degree)}^2\) .

Решение:

1. \(\sin 45\degree-\cos 45\degree+\tg 45\degree=\dfrac{\sqrt{2}}{2}-\) _____ \(+\) _____ \(=\) _____.