Question

Verify the identity. sine x times secant x equals tangent x To verify the​ identity, start with the more complicated side and transform it to look like the other side. Choose the correct transformations and transform the expression at each step.

Answer 1

$\sin x \times \sec x=\tan x,$ proved.

Step-by-step explanation:

To verify, the identity $\sin x \times \sec x=\tan x$.

L.H.S. $=\sin x \times \sec x$

We know that,

$\sec A\cos A=1$

⇒ $\sec A=\dfrac{1}{\cos A}$

Now, L.H.S., becomes

$=\sin x \times \dfrac{1}{\cos x}$

$=\dfrac{\sin x}{\cos x}$

= $\tan x$

= R.H.S., verify.

Thus, $\sin x \times \sec x=\tan x,$ proved.