What is the general solution for sin(x)+1=2cos^2(x) ?

The general solution for sin(x)+1=2cos^2(x) is x= pi/6+2pin,x=(5pi)/6+2pin,x=(3pi)/2+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(x)+1=2cos^2(x)

sin (x) + 1 = 2 cos^{2} (x)

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

sin (x) + 1 = 2 cos^{2} (x)

Subtract

2 cos^{2} (x)

from both sides

sin (x) + 1 - 2 cos^{2} (x) = 0

Rewrite using trig identities

- 1 + sin (x) + 2 sin^{2} (x) = 0

Solve by substitution

sin (x) = \frac{1}{2}, sin (x) = - 1

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

x, arctan (x^{2} + 9 y^{2} - 2 x - 36 y + 37) = 0

sin (5 x) = sin (x)

cos (θ) = \frac{5}{3}

arcsin (x) = \frac{1}{2}

4 tan (x) = 4

What is the general solution for sin(x)+1=2cos^2(x) ?
The general solution for sin(x)+1=2cos^2(x) is x= pi/6+2pin,x=(5pi)/6+2pin,x=(3pi)/2+2pin