Question

How do I verify an identity?

cotx + tanx = secxcscx

Answer 1

I know cot and tan are reciprocals of each other.

Answer 2

change everything to sine and cosine. Then let x = sin(x) and y = cos(x)

Afterwards, you'll have something that resembles simple algebraic fractions.

Answer 3

cos(theta)/sin(theta) + sin(theta)/cos(theta) = 1/(cos theta) * (1/sin(theta)

Answer 4

yes, which means

y/x + x/y = 1/(xy)

Answer 5

also, remember that in this context x^2 + y^2 = 1

Answer 6

so it'd be

y/x + x/y = x^2+y^2/xy?

Answer 7

y/x + x/y = (x^2+y^2)/xy

Answer 8

And then the next step is obvious hopefully

Answer 9

To... simplify it so that it is obvious that it is either a false or true statement?

Answer 10

If you're "verifying an identity", then it already is a true statement.

Answer 11

You just have to come up with the steps to show it. Which for the most part, we've already done.

Answer 12

All you have to do now is just take all those x's and y's and convert them back to sine and cosine.

Answer 13

Basically, what I showed you above is what you'd perhaps write on a piece of scratch paper.

Answer 14

But when you turn in your work, it should look like trig not algebra.

Answer 15

So, changing it back...

do I just convert it back to the original thing we had?

Answer 16

cos/sin + sin/cos = (sin^2 + cos^2)/(sin)(cos)

Answer 17

And then...

If I multiply both sides by sin and cos, then I'm looking at

cos^2 + sin^2 = (sin^2 + cos^2)

since both are even...

Answer 18

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