Question

Tylko 11 )
zadanie b,c,d
Dam najjjjj

Answer 1

Verified answer

Odpowiedź:

W załączniku.

Szczegółowe wyjaśnienie:

Answer 2

11.

b)

[tex]sin \ \alpha = sin(90^{o}-\alpha)\\\\sin \ \alpha = cos \ \alpha \ \ \ /:cos \ \alpha\\\\\frac{sin \ \alpha}{cos \ \alpha} = 1\\\\tg \ \alpha = 1\\\\\boxed{\alpha = 45^{o}}[/tex]

c)

[tex]tg \ \alpha=3tg(90^{o}-\alpha)\\\\tg \ \alpha = 3ctg \ \alpha \ \ \ |\cdot tg \ \alpha\\\\tg \ \alpha\cdot tg \ \alpha = 3ctg \ \alpha\cdot tg \ \alpha\\\\tg^{2} \ \alpha = 3\\\\tg \ \alpha = \sqrt{3}\\\\\boxed{\alpha = 60^{o}}[/tex]

d)

[tex]2 - tg \ \alpha = tg25^{o}\cdot tg(90^{o}-25^{o})\\\\2-tg \ \alpha = tg25^{o}\cdot ctg25^{o}\\\\2-tg \ \alpha = 1 \ \ \ |-2\\\\-tg \ \alpha = -1 \ \ \ |:(-1)\\\\tg \ \alpha = 1\\\\\boxed{\alpha = 45^{o}}[/tex]

Wyjaśnienie:

[tex]sin(90^{o}-\alpha) = cos \ \alpha\\\\tg(90^{o}-\alpha) = ctg \ \alpha[/tex]

[tex]tg \ a\lpha\cdot ctg \ \alpha = 1[/tex]