Answer:
[tex]\tan(x + 40) = 1.842[/tex]
Step-by-step explanation:
Given
[tex]\sin(x + 4) = \cos(3x)[/tex]
Required
Find [tex]\tan(x + 40)[/tex]
In trigonometry
If [tex]\sin(A) = \cos(B)[/tex]
Then: [tex]A + B = 90[/tex]
So, we have:
[tex]\sin(x + 4) = \cos(3x)[/tex]
[tex]3x + x + 4 = 90[/tex]
[tex]4x + 4 = 90[/tex]
Collect like terms
[tex]4x =- 4 + 90[/tex]
[tex]4x =86[/tex]
Solve for x
[tex]x = 86/4[/tex]
[tex]x = 21.5[/tex]
So:
[tex]\tan(x + 40) = \tan(21.5+40)[/tex]
[tex]\tan(x + 40) = \tan(61.5)[/tex]
Using a calculator:
[tex]\tan(x + 40) = 1.842[/tex]
