X. Поставьте вопросы на развитие содержания следующих предложений: 1. Mr. Petrov has gone on business. 2. All the passengers enjoyed their flight. 3. My friend went through the Customs at London airport. 4. Our plane landed at Sheremetievo airport at 11 p.m. 5. He had got instructions before he went abroad. 6. Last night I was at the theatre.

ртпооаоаьмо вгаьвоьаьсsinx + cos x + sin2x = 1

sin x + cos x + 2sinx cosx -1=0

sin x + cos x +2sinx cosx -(sin²x+cos²x)=0

(sin x + cos x) + 2sinx cos x - (sin²x+cos²x+2sinx cosx -2sinx cos x)=0

(sin x+ cos x)+2sinx cosx - (sin x + cos x)² +2sinx cosx=0

(sin x + cos x)² + (sinx + cosx)+4sinxcosx=0

Пусть sin x + cos x = t причем (-√2 ≤ t ≤ √2), тогда возведем оба части до квадрата, имеем

(sin x + cos x)² = t²

1+2sinx cosx = t²

2sinxcosx = t²-1

Заменяем

t²+t+2*(t²-1)=0

t²+t+2t²-2=0

3t²+t-2=0

D=1+24 = 25

t1=(-1+5)/6=2/3

t2=(-1-5)/6 = -1

Возвращаем к замене

\begin{gathered}\sin x+\cos =-1\\ \sqrt{2} \sin(x+ \frac{\pi}{4} )=-1 \\ \sin(x+ \frac{\pi}{4} )=- \frac{1}{ \sqrt{2} } \\ x+ \frac{\pi}{4}=(-1)^{n+1} \frac{\pi}{4}+ \pi n,n \in Z\\ x=(-1)^{n+1} \frac{\pi}{4}- \frac{\pi}{4}+ \pi n,n \in Z\end{gathered}

sinx+cos=−1

2

sin(x+

4

π

)=−1

sin(x+

4

π

)=−

2

1

x+

4

π

=(−1)

n+1

4

π

+πn,n∈Z

x=(−1)

n+1

4

π

−

4

π

+πn,n∈Z

\begin{gathered}\sin x+\cos x= \frac{2}{3} \\ \sqrt{2} \sin(x+ \frac{\pi}{4})= \frac{2}{3} \\ \sin (x+ \frac{\pi}{4})= \frac{ \sqrt{2} }{3} \\ x=(-1)^n\arcsin( \frac{ \sqrt{2} }{3} )- \frac{\pi}{4}+ \pi n,n \in Z\end{gathered}

sinx+cosx=

3

2

2

sin(x+

4

π

)=

3

2

sin(x+

4

π

)=

3

2

x=(−1)

n

arcsin(

3

2

)−

4

π

+πn,n∈Z