If 4 cos theta = 3 then find sin theta and tan theta

1.	If 4 cos theta = 3 then find sin theta and tan theta
Answer» GIVEN :– $\\ \implies \rm 4 \cos(\theta) = 3\\$ TO FIND :– • Value of tan(θ) & sin(θ) = ? SOLUTION :– $\\ \implies \rm 4 \cos(\theta) = 3\\$ $\\ \implies \rm \cos(\theta) = \dfrac{3}{4}\\$ • We know that – $\\ \longrightarrow \sf \green {\sin^{2}( \theta) + \cos^{2} (\theta) = 1}\\$ $\\ \implies \tt {\sin^{2}( \theta) + \left ( \dfrac{3}{4} \right)^{2} = 1}\\$ $\\ \implies \tt {\sin^{2}( \theta) +\dfrac{9}{16}= 1}\\$ $\\ \implies \tt \sin^{2}( \theta) = 1 - \dfrac{9}{16}\\$ $\\ \implies \tt \sin^{2}( \theta) = \dfrac{16 - 9}{16}\\$ $\\ \implies \tt \sin^{2}( \theta) = \dfrac{7}{16}\\$ $\\ \implies \tt \sin( \theta) = \pm \sqrt \dfrac{7}{16}\\$ $\\ \implies \large \red{ \boxed{\tt \sin( \theta) = \pm \dfrac{ \sqrt7}{4}}}\\$ • We also know that — $\\ \longrightarrow \sf \green { \tan( \theta) = \dfrac{ \sin( \theta) }{ \cos( \theta) } } \\$ $\\ \implies \tt { \tan( \theta) = \dfrac{\pm \dfrac{ \sqrt7}{4}}{\dfrac{3}{4}}} \\$ $\\ \implies \large\red { \boxed{\tt { \tan( \theta) = \pm\dfrac{\sqrt{7} }{3}}}}\\$

Answer»

GIVEN :–

$\\ \implies \rm 4 \cos(\theta) = 3\\$