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

The general solution for 2-sin(x)tan(x)=cos(x) is x= pi/3+2pin,x=(5pi)/3+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2-sin(x)tan(x)=cos(x)

2 - sin (x) tan (x) = cos (x)

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

Solution steps

2 - sin (x) tan (x) = cos (x)

Subtract

cos (x)

from both sides

2 - sin (x) tan (x) - cos (x) = 0

Express with sin, cos

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

Rewrite using trig identities

2 cos (x) - 1 = 0

Move

1

to the right side

2 cos (x) = 1

Divide both sides by

2

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

General solutions for

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

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

tan (2 x - \frac{n}{4}) = - 1, 0^{\circ} < x \leq 36 0^{\circ}

2 sin^{2} (θ) = cos^{2} (θ)

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

x, y + arctan (\frac{y}{x}) = 0

tan (θ) = - 1, 0 \leq θ \leq 2 π

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