Question

If Sinθ / Cosθ = 3/4 then Cot θ = ? , Sec θ = ?​

Answer 1

$\rm{\sin\theta/\cos\theta=3/4\quad...\:Given\:Value\:In\:Question}$

$\longrightarrow\rm{\tan\theta=3/4\quad...\:Since\:\sin\theta/\cos\theta=\tan\theta}$

$\rule{315}{2}$

$\longrightarrow\rm{\cot\theta=4/3\quad...\:Since\:\cot\theta=1/\tan\theta}$

$\longrightarrow\rm{\sec\theta=\sqrt{1+\tan^2\theta}\quad...\:Since\:1+\tan^2\theta=\sec^2\theta }$

$\longrightarrow\rm{\sec\theta=\sqrt{1+(3/4)^2}\quad...\:Since\:\tan\theta=3/4 }$

$\longrightarrow\rm{\sec\theta=\sqrt{1+9/16}=\sqrt{16/16+9/16}=\sqrt{25/16}}=5/4$