Answer:
True
Step-by-step explanation:
By the definition,
[tex]\sin A=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{BC}{AB}=\dfrac{a}{c},\\ \\\cos B=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{BC}{AB}=\dfrac{a}{c}[/tex]
So, [tex]\sin A=\cos B.[/tex]
[tex]\csc A=\dfrac{\text{hypotenuse}}{\text{opposite leg}}=\dfrac{AB}{BC}=\dfrac{c}{a},\\ \\\sec B=\dfrac{\text{hypotenuse}}{\text{adjacent leg}}=\dfrac{AB}{BC}=\dfrac{c}{a}[/tex]
Thus, [tex]\cos A=\sec B.[/tex]
[tex]\tan A=\dfrac{\text{opposite leg}}{\text{adjacent leg}}=\dfrac{BC}{AC}=\dfrac{a}{b},\\ \\\cot B=\dfrac{\text{adjacent leg}}{\text{opposite leg}}=\dfrac{BC}{AC}=\dfrac{a}{b}.[/tex]
Thus, [tex]\tan A=\cot B.[/tex]
