What is the general solution for sin(B)+cos(B)=sqrt(2) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(B)+cos(B)=sqrt(2)

sin (B) + cos (B) = 2

B = 2 πn + \frac{π}{4}

Solution steps

sin (B) + cos (B) = 2

Rewrite using trig identities

2 sin (B + \frac{π}{4}) = 2

Divide both sides by

2

sin (B + \frac{π}{4}) = 1

General solutions for

sin (B + \frac{π}{4}) = 1

B + \frac{π}{4} = \frac{π}{2} + 2 πn

Solve

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

B = 2 πn + \frac{π}{4}

3 sin (x) + cos (2 x) = 2

cos (3 x) + cos (5 x) = cos (x)

sin (θ) + sin (θ) cos (θ) = 0

8 + 4 cos (2 x) = 12 cos (x)

tan (x) = - sec (x)

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