What is the general solution for cos(7x)cos(2x)+sin(7x)sin(2x)= 1/2 ?

The general solution for cos(7x)cos(2x)+sin(7x)sin(2x)= 1/2 is x= pi/(15)+(2pin)/5 ,x= pi/3+(2pin)/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(7x)cos(2x)+sin(7x)sin(2x)= 1/2

cos (7 x) cos (2 x) + sin (7 x) sin (2 x) = \frac{1}{2}

x = \frac{π}{15} + \frac{2 πn}{5}, x = \frac{π}{3} + \frac{2 πn}{5}

Solution steps

cos (7 x) cos (2 x) + sin (7 x) sin (2 x) = \frac{1}{2}

Rewrite using trig identities

cos (7 x - 2 x) = \frac{1}{2}

General solutions for

cos (7 x - 2 x) = \frac{1}{2}

7 x - 2 x = \frac{π}{3} + 2 πn, 7 x - 2 x = \frac{5 π}{3} + 2 πn

Solve

7 x - 2 x = \frac{π}{3} + 2 πn : x = \frac{π}{15} + \frac{2 πn}{5}

Solve

7 x - 2 x = \frac{5 π}{3} + 2 πn : x = \frac{π}{3} + \frac{2 πn}{5}

x = \frac{π}{15} + \frac{2 πn}{5}, x = \frac{π}{3} + \frac{2 πn}{5}

sin (2 x) = \frac{1}{2}, 0 \leq x \leq 2 π

8 sin^{2} (θ) - 6 = 0

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

3 cos (x) tan^{2} (x) = cos (x)

cos (x) = cos (3 x)

What is the general solution for cos(7x)cos(2x)+sin(7x)sin(2x)= 1/2 ?
The general solution for cos(7x)cos(2x)+sin(7x)sin(2x)= 1/2 is x= pi/(15)+(2pin)/5 ,x= pi/3+(2pin)/5