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

The general solution for cos(x)=2sin^2(x) is x=0.67488…+2pin,x=2pi-0.67488…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = 0.67488 \dots + 2 πn, x = 2 π - 0.67488 \dots + 2 πn

Solution steps

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

Subtract

2 sin^{2} (x)

from both sides

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

Rewrite using trig identities

cos (x) - (1 - cos^{2} (x)) \cdot 2 = 0

Solve by substitution

cos (x) = \frac{- 1 + 17}{4}, cos (x) = \frac{- 1 - 17}{4}

cos (x) = \frac{- 1 + 17}{4} : x = arccos (\frac{- 1 + 17}{4}) + 2 πn, x = 2 π - arccos (\frac{- 1 + 17}{4}) + 2 πn

cos (x) = \frac{- 1 - 17}{4} :

No Solution

Combine all the solutions

x = arccos (\frac{- 1 + 17}{4}) + 2 πn, x = 2 π - arccos (\frac{- 1 + 17}{4}) + 2 πn

Show solutions in decimal form

x = 0.67488 \dots + 2 πn, x = 2 π - 0.67488 \dots + 2 πn

cos^{2} (x) - sin^{2} (x) = 2 - 5 cos (x)

tan (\frac{x}{4}) = - 3

8 sin^{2} (x) - 2 sin (x) - 1 = 0, - \frac{π}{2} < x < \frac{π}{2}

cos (4 x) - cos (3 x) = 0

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

What is the general solution for cos(x)=2sin^2(x) ?
The general solution for cos(x)=2sin^2(x) is x=0.67488…+2pin,x=2pi-0.67488…+2pin