# Help with trig proof identities c3 Please

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#1
Prove the follow:

(Sec^2 x + tan^2 x) (cosec^2 x + cot^2 x) = 1 + 2sec^2 xcosec^2 x

So I've replaced tan squared x and cot squared x with their identities (e.g. sec squared x minus 1). And then i've expanded the brackets but I get:

4sec^2 xcosec x - 2sec^2 x - 2cosec^2 x + 1

Which isn't the identity I had to get to and Im not sure what to do from here. Any help would be greatly appreciated - thanks.
0
3 years ago
#2
(Original post by MrToodles4)
Prove the follow:

(Sec^2 x + tan^2 x) (cosec^2 x + cot^2 x) = 1 + 2sec^2 xcosec^2 x

So I've replaced tan squared x and cot squared x with their identities (e.g. sec squared x minus 1). And then i've expanded the brackets but I get:

4sec^2 xcosec x - 2sec^2 x - 2cosec^2 x + 1

Which isn't the identity I had to get to and Im not sure what to do from here. Any help would be greatly appreciated - thanks.
How about you just express the first and second brackets as fractions in terms of sin and cons, and THEN multiply them together, and then simplify?
0
3 years ago
#3
Otherwise, you need to convince yourself that
0
3 years ago
#4
(Original post by MrToodles4)
Prove the follow:

(Sec^2 x + tan^2 x) (cosec^2 x + cot^2 x) = 1 + 2sec^2 xcosec^2 x

So I've replaced tan squared x and cot squared x with their identities (e.g. sec squared x minus 1). And then i've expanded the brackets but I get:

4sec^2 xcosec x - 2sec^2 x - 2cosec^2 x + 1

Which isn't the identity I had to get to and Im not sure what to do from here. Any help would be greatly appreciated - thanks.
There are numerous ways to start this.

Personally, I would just multiply out the brackets first and look for a couple of terms that are what you want to see on the RHS. There are a couple of terms left that aren't quite what you want, so you need to try to manipulate them into the correct format...
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#5
(Original post by RDKGames)
Otherwise, you need to convince yourself that
Sorry, what do you mean exactly here?
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#6
(Original post by davros)
There are numerous ways to start this.

Personally, I would just multiply out the brackets first and look for a couple of terms that are what you want to see on the RHS. There are a couple of terms left that aren't quite what you want, so you need to try to manipulate them into the correct format...
Yeah I've tried but Im not sure how to
0
3 years ago
#7
(Original post by MrToodles4)
Yeah I've tried but Im not sure how to
Use and rewrite the expression.
0
#8
(Original post by Desmos)
Use and rewrite the expression.
Yeah I've been using this - still not getting anywhere sadly
0
3 years ago
#9
(Original post by MrToodles4)
Sorry, what do you mean exactly here?
Clearly what you've done is correct, but for your expression to be equivalent to then it is only possible if

Once you've proven this, then you can finish it off in your original working.
0
3 years ago
#10
(Original post by MrToodles4)
Yeah I've tried but Im not sure how to
Do you agree that if you multiply out you get this:

You want to keep hold of the 1st term because it's going to contribute to the RHS you're trying to get to, and you should be able to simplify the 4th term immediately from the definitions of tan and cot.

So what can you do with the 2nd and 3rd terms?
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