Question

prove: cos thita - sin thita/cos thita = 1 - tan thita​

Answer 1

To prove :-

${\dashrightarrow \dfrac{ \cos \theta - \sin \theta}{ \cos \theta} = 1 - \tan \theta}$

Solution :-

${\dashrightarrow \dfrac{ \cos \theta - \sin \theta}{ \cos \theta} = 1 - \tan \theta}$

${\dashrightarrow \bigg(\dfrac{ \cos \theta }{ \cos \theta} - \dfrac{ \sin \theta}{ \cos \theta} \bigg)= 1 - \tan \theta}$

${\dashrightarrow \bigg( \cancel\dfrac{ \cos \theta }{ \cos \theta} - \dfrac{ \sin \theta}{ \cos \theta} \bigg)= 1 - \tan \theta}$

${\dashrightarrow \bigg(1 - \dfrac{ \sin \theta}{ \cos \theta} \bigg)= 1 - \tan \theta}$

» Apply formula sin A/cos A= tan A

${\dashrightarrow (1 - \tan \theta)= 1 - \tan \theta}$

${\dashrightarrow \boxed{1 - \tan \theta= 1 - \tan \theta}}$

» LHS = RHS

Hence proved

Answer 2

$\frac{cos \theta - sin \theta}{cos \theta} \\ = \frac{cos \theta}{cos \theta} - \frac{sin \theta}{cos \theta} \\ = 1 - tan \theta$