Question

find one solution for the equation. assume that all angles involved are acute angles. tan(2b - 12°)=cot(5b - 10°) b = □° (simplify your answer.)

Explanation:

Step1: Use co - function identity

We know that $\tan\theta=\cot(90^{\circ}-\theta)$. So, $\tan(2B - 12^{\circ})=\cot(90^{\circ}-(2B - 12^{\circ}))$. The given equation $\tan(2B - 12^{\circ})=\cot(5B - 10^{\circ})$ implies $90^{\circ}-(2B - 12^{\circ})=5B - 10^{\circ}$.

Step2: Simplify the equation

Expand the left - hand side: $90^{\circ}-2B + 12^{\circ}=5B - 10^{\circ}$. Combine like terms: $102^{\circ}-2B=5B - 10^{\circ}$.

Step3: Solve for B

Add $2B$ to both sides: $102^{\circ}=5B - 10^{\circ}+2B$, which simplifies to $102^{\circ}=7B - 10^{\circ}$. Then add $10^{\circ}$ to both sides: $102^{\circ}+10^{\circ}=7B$, so $112^{\circ}=7B$. Divide both sides by 7: $B = 16^{\circ}$.

Answer:

$16$