What is the general solution for 5cos(2x+3)=sin(2x+3) ?

The general solution for 5cos(2x+3)=sin(2x+3) is x=(1.37340…)/2+(pin)/2-3/2

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5cos(2x+3)=sin(2x+3)

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

x = \frac{1.37340 \dots}{2} + \frac{πn}{2} - \frac{3}{2}

Degrees

x = - 46.59863 \dots^{\circ} + 9 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

cos (2 x + 3), cos (2 x + 3) \neq = 0

\frac{5 cos ( 2 x + 3 )}{cos ( 2 x + 3 )} = \frac{sin ( 2 x + 3 )}{cos ( 2 x + 3 )}

Simplify

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

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

5 = tan (2 x + 3)

Switch sides

tan (2 x + 3) = 5

tan (2 x + 3) = 5

Apply trig inverse properties

tan (2 x + 3) = 5

General solutions for

tan (2 x + 3) = 5

tan (x) = a \Rightarrow x = arctan (a) + πn

2 x + 3 = arctan (5) + πn

2 x + 3 = arctan (5) + πn

Solve

2 x + 3 = arctan (5) + πn : x = \frac{arctan ( 5 )}{2} + \frac{πn}{2} - \frac{3}{2}

2 x + 3 = arctan (5) + πn

Move

3

to the right side

2 x + 3 = arctan (5) + πn

Subtract

3

from both sides

2 x + 3 - 3 = arctan (5) + πn - 3

Simplify

2 x = arctan (5) + πn - 3

2 x = arctan (5) + πn - 3

Divide both sides by

2

2 x = arctan (5) + πn - 3

Divide both sides by

2

\frac{2 x}{2} = \frac{arctan ( 5 )}{2} + \frac{πn}{2} - \frac{3}{2}

Simplify

x = \frac{arctan ( 5 )}{2} + \frac{πn}{2} - \frac{3}{2}

x = \frac{arctan ( 5 )}{2} + \frac{πn}{2} - \frac{3}{2}

x = \frac{arctan ( 5 )}{2} + \frac{πn}{2} - \frac{3}{2}

Show solutions in decimal form

x = \frac{1.37340 \dots}{2} + \frac{πn}{2} - \frac{3}{2}

4 \cdot cos (x) + 3 \cdot sec (x) = 8

\frac{3}{5} = sin (x)

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

cos^{2} (x) + cos^{3} (x) + cos^{4} (x) + cos^{5} (x) = 0

sin^{2} (x) - 4 sin (x) = - 3

What is the general solution for 5cos(2x+3)=sin(2x+3) ?
The general solution for 5cos(2x+3)=sin(2x+3) is x=(1.37340…)/2+(pin)/2-3/2