What is the general solution for (7sin(2x)+7cos(2x))^2=49 ?

The general solution for (7sin(2x)+7cos(2x))^2=49 is x=pin+pi/2 ,x=pin+(3pi)/4 ,x=pin,x=pin+pi/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(7sin(2x)+7cos(2x))^2=49

(7 sin (2 x) + 7 cos (2 x))^{2} = 49

x = πn + \frac{π}{2}, x = πn + \frac{3 π}{4}, x = πn, x = πn + \frac{π}{4}

Solution steps

(7 sin (2 x) + 7 cos (2 x))^{2} = 49

Subtract

49

from both sides

(7 sin (2 x) + 7 cos (2 x))^{2} - 49 = 0

Factor

(7 sin (2 x) + 7 cos (2 x))^{2} - 49 : 49 (sin (2 x) + cos (2 x) + 1) (sin (2 x) + cos (2 x) - 1)

49 (sin (2 x) + cos (2 x) + 1) (sin (2 x) + cos (2 x) - 1) = 0

Solving each part separately

sin (2 x) + cos (2 x) + 1 = 0 or sin (2 x) + cos (2 x) - 1 = 0

sin (2 x) + cos (2 x) + 1 = 0 : x = πn + \frac{π}{2}, x = πn + \frac{3 π}{4}

sin (2 x) + cos (2 x) - 1 = 0 : x = πn, x = πn + \frac{π}{4}

Combine all the solutions

x = πn + \frac{π}{2}, x = πn + \frac{3 π}{4}, x = πn, x = πn + \frac{π}{4}

- 1 - tan (x) = sec (x)

5 cos (θ) + 4 = 0

2 sin^{2} (2 θ) = - 1 + 3 sin (2 θ)

6 tan^{2} (θ) + 10 tan (θ) = 9 tan (θ) + 2

y, z = cos (y)

What is the general solution for (7sin(2x)+7cos(2x))^2=49 ?
The general solution for (7sin(2x)+7cos(2x))^2=49 is x=pin+pi/2 ,x=pin+(3pi)/4 ,x=pin,x=pin+pi/4