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Given below are two statements:
Statement I: If $$sin(\theta) =\dfrac{5}{13}$$, then the value of $$tan(\theta)=\dfrac{5}{12}$$
Statement II: If $$cot(\theta) =\dfrac{12}{5}$$, then the value of $$sin(\theta)=\dfrac{5}{12}$$
Statement I
$$sin(\theta) =\dfrac{5}{13}=\dfrac{P}{H}$$
We can assume P = 5k, and H = 13k
$$P^2+B^2=H^2$$
$$25k^2+B^2=169k^2$$
$$B=12k$$
$$tan(\theta)=\dfrac{P}{B}=\dfrac{5}{12}$$
Statement I is true
Statement II
$$cot(\theta) =\dfrac{12}{5}=\dfrac{B}{P}$$
We can assume P = 5k, and H = 12k
$$P^2+B^2=H^2$$
$$25k^2+144k^2=H^2$$
$$H=13k$$
$$sin(\theta)=\dfrac{P}{H}=\dfrac{5}{13}$$
Statement II is false