Core 3 Maths Trig Question?

Question

The question is, simplify the following:

tanx/1+tan^2 x

I already know the answer i just can't get to it.

Please give a full explanation.

Thank you in advance

The answer is sinxcosx by the way. Thanks again

Answer 1

1+tan^2 x = sec^2(x) = 1 / cos^2(x)

tan(x) = sin(x) / cos(x)

The equation becomes

sin(x) / cos(x) divided by 1/cos^2(x)

sin(x) / cos(x) multiplied by cos^2(x)

One cos(x)  cancels with cos^2(x)

= sin(x) cos(x)

Answer 2

Please specify the brackets properly, otherwise the equation would differ.  The expression should be (tan x)/(1+tan^2 x)

tan x = (sin x) / (cos x)

Thus the given expression would become:

[sin x / cos x] / [1 + ( sin ^2 x / cos ^2 x)

= [sin x / cos x] / [(cos ^2 x + sin ^2 x) / cos ^2 x]

But sin ^2 x + cos ^2 x = 1

Thus

==> [sin x / cos x] / [1 / cos ^2 x]

==> sin x         cos ^2 x

       --------   *   -------------

       cos x                    1

==> sin x cos x