question_answer

If cosec\[\theta =\frac{5}{4}\], find the value of \[cot\text{ }\theta \].

Answer:

We know that,

\[co{{t}^{2}}\theta =cose{{c}^{2}}\theta -1\]

\[={{\left( \frac{5}{4} \right)}^{2}}-1\]

\[=\frac{25}{16}-1=\frac{25-16}{16}=\frac{9}{16}\]

\[\Rightarrow {{\cot }^{2}}\theta =\frac{9}{16}\]

\[\Rightarrow \cot \theta =\frac{3}{4}\]