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

The general solution for cos(x)sin(x)= 1/2 is x= pi/4+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(x)sin(x)= 1/2

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

x = \frac{π}{4} + πn

Solution steps

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

Rewrite using trig identities

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

Multiply both sides by

2

sin (2 x) = 1

General solutions for

sin (2 x) = 1

2 x = \frac{π}{2} + 2 πn

Solve

2 x = \frac{π}{2} + 2 πn : x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

(cos (x) - 3) (cos (x) + 1) = 0

4 tan^{2} (x) - 16 tan (x) + 7 = 0

1 - cos (x) = 0.5

arctan (100 x) - arctan (x) = 4 5^{\circ}

tan^{2} (x) - 9 = 0

What is the general solution for cos(x)sin(x)= 1/2 ?
The general solution for cos(x)sin(x)= 1/2 is x= pi/4+pin