Question

Simplify the following Trigonometric Identity:
tanx*cos^2x

- Show work, if possible using the tool of draw in order for me to understand the process step by step please :(

Answer 1

Substitute tan(x) with sin(x) / cos(x) and simplify.
The cos(x) in the denominator will cancel out one of the cos(x) in cos^2(x).

Answer 2

I still don't get it! @ranga :(

Answer 3

could you be more specific? @ranga

Answer 4

\[\tan(x)\cos^2(x) = \frac{ \sin(x) }{ \cos(x) }\cos^2(x) = \sin(x)\cos(x) = \frac{ \sin(2x) }{ 2 }\]

Answer 5

Am I doing it right? What's the next step?

Answer 6

The last step is optional. IDK if they have taught you double angle formula.
If not, you can stop the answer at sin(x)cos(x)

Answer 7

\[\frac{ \sin(x) }{ \cos(x)}\cos^2(x) = \frac{ \sin(x) }{ \cos(x)}\cos(x)\cos(x) = \sin(x)\cos(x)\]

Answer 8

Is it ok? @ranga

Answer 9

The last pic is too small to read.

Answer 10

what about this one?

Answer 11

@ranga

Answer 12

I'd write it like this:
tanx*cos^2x =
sin(x)/cos(x) * cos(x) * cos(x) =
sin(x)cos(x)

Answer 13

could you write it in a paper and send me a picture of it please? :(

Answer 14

@ranga

Answer 15

\[\tan(x)\cos^2(x) = \\ \frac{\sin(x) }{ \cos(x) }\cos(x)\cos(x) = \\ \sin(x)\cos(x) \]

Answer 16

like that? @ranga

Answer 17

You write it just like I did in my previous reply.
Three lines.

If you wish to show "cancelling terms", on the second line in my previous reply, you can cross out the cos(x) in the denominator and cross out one cos(x) in the numerator.