What is the general solution for cos(x+60)=sin(x) ?

The general solution for cos(x+60)=sin(x) is x=0.26179…+180n

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cos(x+60)=sin(x)

cos (x + 6 0^{\circ}) = sin (x)

x = 0.26179 \dots + 18 0^{\circ} n

Solution steps

cos (x + 6 0^{\circ}) = sin (x)

Rewrite using trig identities

\frac{1}{2} cos (x) - \frac{3}{2} sin (x) = sin (x)

Subtract

sin (x)

from both sides

\frac{1}{2} cos (x) + \frac{- 3 - 2}{2} sin (x) = 0

Simplify

\frac{1}{2} cos (x) + \frac{- 3 - 2}{2} sin (x) : \frac{cos ( x ) + ( - 3 - 2 ) sin ( x )}{2}

\frac{cos ( x ) + ( - 3 - 2 ) sin ( x )}{2} = 0

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

cos (x) + (- 3 - 2) sin (x) = 0

Rewrite using trig identities

1 - (2 + 3) tan (x) = 0

Move

1

to the right side

- (2 + 3) tan (x) = - 1

Simplify

- (2 + 3) : - 2 - 3

(- 2 - 3) tan (x) = - 1

Divide both sides by

- 2 - 3

tan (x) = 2 - 3

Apply trig inverse properties

x = arctan (2 - 3) + 18 0^{\circ} n

Show solutions in decimal form

x = 0.26179 \dots + 18 0^{\circ} n

csc^{2} (x) = 2 cot^{2} (x)

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

5 sin (x) cos (x) + 4 cos (x) = 0

2 sin (x) = 4 cos (x)

6 arcsin (x) = 2 π

What is the general solution for cos(x+60)=sin(x) ?
The general solution for cos(x+60)=sin(x) is x=0.26179…+180n