Answer:
[tex]x=16[/tex]
Step-by-step explanation:
We have been given that [tex]\text{sin}(x+21)^{\circ}=\text{cos}(2x+21)^{\circ}[/tex]. We are asked to find the value of x.
We know that [tex]\text{sin}(\theta)=\text{cos}(90-\theta)[/tex] and these both angles add up-to 90 degrees. So we can set an equation as:
[tex]x+21+2x+21=90[/tex]
[tex]3x+42=90[/tex]
Upon subtracting 42 from both sides of our equation we will get,
[tex]3x+42-42=90-42[/tex]
[tex]3x=48[/tex]
Let us divide both sides of our equation by 3.
[tex]\frac{3x}{3}=\frac{48}{3}[/tex]
[tex]x=16[/tex]
Therefore, the value of x is 16.
