Question

Sec^2 theta/tan theta = sec theta x csc theta

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

• tan x = $\frac{sinx}{cosx}$

• sec x = $\frac{1}{cosx}$, csc x = $\frac{1}{sinx}$

Consider the left side with x = Θ

$\frac{sec^2x}{tanx}$

=$\frac{1/cos^2x}{\frac{sinx}{cosx} }$

= $\frac{1}{cos^2x}$ × $\frac{cosx}{sinx}$

= $\frac{1}{cosxsinx}$

= $\frac{1}{cosx}$ × $\frac{1}{sinx}$

= secxcscx = right side ⇒ verified