Question

prove that $\\\dfrac{\sin\theta}{\cos\theta}=\dfrac{\sec\theta}{\csc\theta}$​

Answer 1

Answer:

$lhs \: = \frac{ \sin( \theta) }{cos \theta} \: \\ \ sin{ \theta} \: = \: \frac{opp}{hyp} \\ \cos{ \theta} = \frac{adj}{hyp} \: \: \\ \frac{ \sin( \theta) }{ \cos( \theta) } = \frac{opp}{hyp} \times \frac{hyp}{adj } = \frac{opp}{adj} \\ \: \: \: \: \: \: = \tan( \theta) \\ rhs \: = \frac{ \sec( \theta) }{ \csc( \theta) } = \frac{ \frac{hyp}{adj} }{ \frac{hyp}{opp} } \\ = \frac{hyp}{adj} \times \frac{opp}{hyp} = \frac{opp}{adj} = \tan( \theta)$

hence proved......

Answer 2

Step-by-step explanation:

this is proved that left hand side= right hand side