PdHHE

Išspręskite lygtį $$sin(x)\cdot ctg(x) = 1$$

Sprendimas.

 sin(x)* ctg(x)  = 
1

 sin(x)* ctg(x) = 1$$sin(x)\cdot ctg(x)$$ = $$1$$

$${\normalsize ctg(x)}$$ = $${\normalsize \frac{cos(x)}{sin(x)}}$$

 

sin(x)* cos(x)

/ sin(x)

 = 1$$\frac{sin(x)\cdot cos(x)}{sin(x)}$$ = $$1$$

$${\normalsize \frac{sin(x)\cdot cos(x)}{sin(x)}}$$ = $${\normalsize cos(x)}$$

cos(x) = 1$$cos(x)$$ = $$1$$

arccos(cos(x)) = arccos(1)$$arccos(cos(x))$$ = $$arccos(1)$$

$${\normalsize arccos(cos(x))}$$ = $${\normalsize x}$$

x = arccos(1)$$x$$ = $$arccos(1)$$

$${\normalsize arccos(1)}$$ = $$0$$

x = 0$$x$$ = $$0$$

$$sin(x)\cdot ctg(x)$$  = $$1$$

$$\frac{sin(x)\cdot cos(x)}{sin(x)}$$  = $$1$$

$$cos(x)$$  = $$1$$

$$x$$  = $$0$$

sin(x)*ctg(x)  =  1

sin(x)*cos(x)/sin(x)  =  1

cos(x)  =  1

x  =  0

gavome x = 0.

Kadangi $$ctg(x) = \frac{cos(x)}{sin(x)}$$,

esantis vardiklyje sin(x) negali būti lygus 0

sin(x) ≠ 0,

x ≠ 0.

Atsakymas: sprendinių nėra