Question

need to simplify 2cosαsinα/cos^2α+1-sin^2α

Answer 1

You need to precisely define what you mean by simplify

Answer 2

\[\frac{ 2cosasina }{ \cos ^{2}a } + 1-\sin ^{2}a\]
Correct or no?

Answer 3

Weather or not something is simple depends on the context

Answer 4

i meant" when it is defined"

Answer 5

When what is defined?

Answer 6

Whenever "2cosαsinα/cos^2α+1-sin^2α" is defined, it simplifies to what.
I know the answer is tan but dont know how to to get sin/cos out of this equation

Answer 7

You still haven't properly defined 'simplify' note that all 4 of these expressions are equivalent, but which one is 'simple' is a matter of opinion unless otherwise specified.
$$a$$
$$a+5-5$$
$$5(\frac{a}{5}+1)-5$$
$$5(\frac{a}{5}+1)-\frac{120}{4}$$

Answer 8

psymon- all of cos^2α+1-sin^2α is the denominator

Answer 9

For example, take $$7+\frac{1}{23}$$
And
$$\frac{162}{23}$$
I might say that the first one is simpler in the sense I can see that its clearly very close to 7, while others might say the second one is simple because it is in the form of a fraction, you need to properly define what you mean when you say 'simplify'.

Answer 10

I want to simplify it to equal tan (or to sin/cos)

Answer 11

Ok, its equal to tan(x)

Answer 12

$$\sin(x)^2+\cos(x)^2=1$$

Answer 13

$$\cos(x)^2=1-\sin(x)^2$$

Answer 14

$$2\cos(x)^2=1+\cos(x)^2-sin(x)^2$$

Answer 15

Which is the expression in your denominator

Answer 16

so we have $$\frac{2\cos(x)\sin(x)}{\cos(x)^2+1-\sin(x)^2}=\frac{2\cos(x)\sin(x)}{2\cos(x)^2}=\frac{\cos(x)\sin(x)}{\cos(x)^2}=\frac{\sin(x)}{\cos(x)}=\tan(x)$$

Answer 17

@nikkicee As required.