Question

if tan Q = prependicular/base, prove that tan Q= sinQ/cosQ
answer the questions step by step plz

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Answer 1

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies tan \: Q= \frac{Perpendicular}{Base} \\ \\ \red{\underline \bold{To \: Prove :}} \\ \tt: \implies tan \: Q= \frac{sin \: Q}{cos \: Q}$

• According to given question :

$\bold{Proof : } \\ \tt: \implies tan \: Q = \frac{sin \: Q}{cos \: Q} \\ \\ \bold{L.H.S} \\ \tt: \implies tan \: Q = \frac{p}{h} - - - - - (1) \\ \\ \bold{R.H.S} \\ \tt: \implies \frac{sin \: Q}{cos \: Q} = \frac{ \frac{p}{h} }{ \frac{b}{h} } \\ \\ \tt: \implies \frac{sin \: Q}{cos \: Q} = \frac{p}{h} \times \frac{h}{b} \\ \\ \tt: \implies \frac{sin \: Q}{cos \: Q} = \frac{p}{b} - - - - - (2) \\ \\ \bold{From \: eqn \: (1) \: and \: (2)} \\ \green{ \tt: \implies tan \: Q= \frac{sin \: Q}{cos \: Q}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \green{\bold {\huge{\boxed{ \tt Proved}}}}$