What is the general solution for tan(x)sin(x)+sin(-x)=0,0<= x<= 2pi ?

The general solution for tan(x)sin(x)+sin(-x)=0,0<= x<= 2pi is x=0,x=pi,x=2pi,x= pi/4 ,x=(5pi)/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tan(x)sin(x)+sin(-x)=0,0<= x<= 2pi

tan (x) sin (x) + sin (- x) = 0, 0 \leq x \leq 2 π

x = 0, x = π, x = 2 π, x = \frac{π}{4}, x = \frac{5 π}{4}

Solution steps

tan (x) sin (x) + sin (- x) = 0, 0 \leq x \leq 2 π

Rewrite using trig identities

- sin (x) + sin (x) tan (x) = 0

Factor

- sin (x) + sin (x) tan (x) : sin (x) (tan (x) - 1)

sin (x) (tan (x) - 1) = 0

Solving each part separately

sin (x) = 0 or tan (x) - 1 = 0

sin (x) = 0, 0 \leq x \leq 2 π : x = 0, x = π, x = 2 π

tan (x) - 1 = 0, 0 \leq x \leq 2 π : x = \frac{π}{4}, x = \frac{5 π}{4}

Combine all the solutions

x = 0, x = π, x = 2 π, x = \frac{π}{4}, x = \frac{5 π}{4}

tan (\frac{2 x}{3}) + 3 = 0

cos (x + \frac{3 π}{4}) - cos (x - \frac{3 π}{4}) = 0

tan (x) = \frac{50}{100}

sin (- x) = 0

cos (x) = \frac{4}{6}

What is the general solution for tan(x)sin(x)+sin(-x)=0,0<= x<= 2pi ?
The general solution for tan(x)sin(x)+sin(-x)=0,0<= x<= 2pi is x=0,x=pi,x=2pi,x= pi/4 ,x=(5pi)/4