7. Розв'яжіть рiвняння 3 cos x + 4 sin x = 3.. Created by gromovaivilina.

7. Розв'яжіть рiвняння 3 cos x + 4 sin x = 3.

July 2023 1 6 Report

7. Розв'яжіть рiвняння
3 cos x + 4 sin x = 3.

Answers & Comments

Kormash
3 cos x + 4 sin x = 3
3 • (1-t^2)/(1+t^2) + 4 • (2t)/(1+t^2) = 3
3 - (3t^2)/(1+t^2) + (8t)/(1+t^2)-3 = 0
(3-3t^2 + 8t-3(1+t^2))/(1+t^2) = 0
(3-3t^2+8t-3-3t^2)/(1+t^2) = 0
(-6t^2+8t)/(1+t^2) = 0
-6t^2+8t = 0
-2t(3t-4) = 0
t(3t-4) = 0
t = 0
3t-4 = 0
3t = 4
t = 4/3
——
tg(x/2) = 0
x = 2пk; k ∈ Z
tg(x/2) = 4/3
x = arctg 4/3 + 2пk, k ∈ Z
Ответ : x = 2пk; k ∈ Z

1 votes Thanks 1

Answers & Comments

9926537cbe99b23072ab349c394c3968

7b751a4d66a79b34fd0b941d60135ba6

59e0bc0e457ddfe83d373ce50fd613d9

9764cbcc6229bd372d3c7ed6640642c9

a265e20c6da0cd9858df9234b6662a22

5ec381dee561474263b7785f4d87fb2f

0bb145006351d09982c79b86450f2c61

1611492d2e7f138b2589d15e410302a9

e1ede5a025e20dd778d2ed05093935a6

4 i ii i i i i i

Helpful Links

Helpful Social