Question

prove tan θ + csc θ/ sec θ= (sec θ) (csc θ)

Answer 1

@Naberh00d, you still here?

Answer 2

yeah can you answer my question

Answer 3

I will HELP you with it.

Answer 4

I will use x instead of theta for convenience. Is that okay?

Answer 5

perfect

Answer 6

\[\tan(x) + \frac{\csc(x)}{\sec(x)} = \sec(x)\csc(x)\]

Answer 7

then we change tan to be sin x /
Cos x

Answer 8

First begin with the LHS:

\[\tan(x) + \frac{\csc(x)}{\sec(x)}\]

Answer 9

Change \(\tan(x)\) to \(\dfrac{\sin(x)}{\cos(x)}\):

\[\dfrac{\sin(x)}{\cos(x)} + \frac{\csc(x)}{\sec(x)}\]

Answer 10

alright keep it going now

Answer 11

Next factor out \(\csc(x)\):

\[\csc(x)\left(\frac{\sin(x)}{\cos(x)} \div \csc(x) + \frac{1}{\sec(x)}\right)\]

Answer 12

why would you do that??

Answer 13

I'll show you. But first, do you understand the result of factoring out \(\csc(x)\)?

Answer 14

yeah but I don't think you need to factor it out

Answer 15

Factoring out makes it easier to solve. Factoring helps to simplify expressions.