[hines57]

((secx-tanx)^2 1)/(secxcscx-tanxcscx)=2tanx

[LuckyChucky13]

Is the first bracket to the power of 21?

[hines57]

sorry its 2+1 ((secx-tanx)^2+1)/(secxcscx-tanxcscx)=2tanx

[LuckyChucky13]

I will try to show it below, if it's not too clear (since it's not mathematically friendly, let me know and I will keep trying:

Here goes:

This is for the numerator (the top part)
First, expand the bracket (that is, multiply it by itself)

So you get: Sec^2 (x) - 2 Sec(x)tan(x) + tan^2(x) + 1
Now, one of the identities is that tan^2(x) + 1 is equal to sec^2(x), s the numerator becomes:

2sec^2(x) - 2sec(x)tan(x)
Now factor out the 2sec(x), which is common to both terms and you get:
2sec(x) {sec(x) - tan(x)}

For the denominator, factor out the csc(x) so you get:
csc(x) {sec(x) - tan(x)}

Cancel the common brackets from the numerator and denominator (which is {sec(x)tan(x)} and you're left with:

2sec(x) / csc(x)

this simplifies to 2 (1/cos(x) / 1/sin(x))
now, when dividing by a fraction, we multiply by its reciprocal, so we get:

2 (1/cos(x) * sin(x)/1)

which simplifies to 2tan(x).

If anything is not clear, let me know...

Good luck.

[LuckyChucky13]

I will try to show it below, if it's not too clear (since it's not mathematically friendly, let me know and I will keep trying:

Here goes:

This is for the numerator (the top part)
First, expand the bracket (that is, multiply it by itself)

So you get: Sec^2 (x) - 2 Sec(x)tan(x) + tan^2(x) + 1
Now, one of the identities is that tan^2(x) + 1 is equal to sec^2(x), s the numerator becomes:

2sec^2(x) - 2sec(x)tan(x)
Now factor out the 2sec(x), which is common to both terms and you get:
2sec(x) {sec(x) - tan(x)}

For the denominator, factor out the csc(x) so you get:
csc(x) {sec(x) - tan(x)}

Cancel the common brackets from the numerator and denominator (which is {sec(x)tan(x)} and you're left with:

2sec(x) / csc(x)

this simplifies to 2 (1/cos(x) / 1/sin(x))
now, when dividing by a fraction, we multiply by its reciprocal, so we get:

2 (1/cos(x) * sin(x)/1)

which simplifies to 2 (sin(x) / cos(x)) and in turn you ger: 2tan(x).

If anything is not clear, let me know...

Good luck.