What is the general solution for solvefor A,cos(pi/3-A)=2sin(A) ?

The general solution for solvefor A,cos(pi/3-A)=2sin(A) is A=0.41528…+pin

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solvefor A,cos(pi/3-A)=2sin(A)

solve for

A, cos (\frac{π}{3} - A) = 2 sin (A)

A = 0.41528 \dots + πn

Solution steps

cos (\frac{π}{3} - A) = 2 sin (A)

Rewrite using trig identities

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

Subtract

2 sin (A)

from both sides

\frac{1}{2} cos (A) + \frac{3 - 4}{2} sin (A) = 0

Simplify

\frac{1}{2} cos (A) + \frac{3 - 4}{2} sin (A) : \frac{cos ( A ) + ( 3 - 4 ) sin ( A )}{2}

\frac{cos ( A ) + ( 3 - 4 ) sin ( A )}{2} = 0

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

cos (A) + (3 - 4) sin (A) = 0

Rewrite using trig identities

1 + (- 4 + 3) tan (A) = 0

Move

1

to the right side

(- 4 + 3) tan (A) = - 1

Divide both sides by

- 4 + 3

tan (A) = \frac{4 + 3}{13}

Apply trig inverse properties

A = arctan (\frac{4 + 3}{13}) + πn

Show solutions in decimal form

A = 0.41528 \dots + πn

- 3 + 3 = 26 cos (θ)

sin (\frac{π}{2} - x) = - 1, 0^{\circ} \leq x \leq 36 0^{\circ}

2 sin (5 x) = - 1

4 sin^{2} (x) + 8 cos (x) - 7 = 0

6 (cos (b))^{2} + cos (b) - 1 = 0

What is the general solution for solvefor A,cos(pi/3-A)=2sin(A) ?
The general solution for solvefor A,cos(pi/3-A)=2sin(A) is A=0.41528…+pin