What is the general solution for cos(a)=sin(a+30) ?

The general solution for cos(a)=sin(a+30) is a=30+180n

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cos(a)=sin(a+30)

cos (a) = sin (a + 3 0^{\circ})

a = 3 0^{\circ} + 18 0^{\circ} n

Solution steps

cos (a) = sin (a + 3 0^{\circ})

Rewrite using trig identities

cos (a) = \frac{3}{2} sin (a) + \frac{1}{2} cos (a)

Subtract

\frac{3}{2} sin (a) + \frac{1}{2} cos (a)

from both sides

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

Simplify

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

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

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

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

Rewrite using trig identities

1 - 3 tan (a) = 0

Move

1

to the right side

- 3 tan (a) = - 1

Divide both sides by

- 3

tan (a) = \frac{3}{3}

General solutions for

tan (a) = \frac{3}{3}

a = 3 0^{\circ} + 18 0^{\circ} n

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

\frac{sin ( 5 0 ^{\circ} )}{10} = \frac{sin ( q )}{12}

271.63 = \frac{3 3 \cdot 169.7}{π} cos (α)

2 sin (t) cos (t) + sin (t) - 2 cos (t) - 1 = 0

4 cos^{2} (\frac{x}{2}) - 3 = 0

What is the general solution for cos(a)=sin(a+30) ?
The general solution for cos(a)=sin(a+30) is a=30+180n