Question

if sin theta=a/b and cos theta=c/d find tan theta and cot theta​

Answer 1

Answer

tanθ = ad/bc

cotθ = bc/ad

Given

• sinθ = a/b
• cosθ = c/d

To Find

• tanθ and cotθ

Solution

We know that ,

$\rm \tan \theta = \dfrac{ \sin \theta }{ \cos \theta } \\ \\ \rm\implies \tan \theta = \dfrac{ \dfrac{a}{b} }{ \dfrac{c}{d} } \\ \\ \rm \implies \tan \theta = \dfrac{a}{b} \times \dfrac{d}{c} \\ \\ \rm\implies \tan \theta = \frac{ad}{bc}$

And again we have ,

$\rm \cot \theta = \dfrac{1}{ \tan \theta} \\ \\ \implies \rm \cot \theta = \dfrac{1}{ \dfrac{ad}{bc} } \\ \\ \rm \implies \cot \theta = \dfrac{bc}{ad}$