annabel_gilmour
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I need to simplify

tan(x)*√(1-sin⁻²(x))

the only two identities I can use are tan(x)=sin(x)/cos(x) and sin²(x)+cos²(x)=1 (these are the only identities in the specification of the course I’m studying)

How would I get rid of the square root?
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RDKGames
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(Original post by annabel_gilmour)
I need to simplify

tan(x)*√(1-sin⁻²(x))

the only two identities I can use are tan(x)=sin(x)/cos(x) and sin²(x)+cos²(x)=1 (these are the only identities in the specification of the course I’m studying)

How would I get rid of the square root?
From the identity sin^2 + cos^2 = 1, you can notice that you will get \sin^{-2}x if you proceed to divide both sides of it by \sin^2 x.
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15Characters...
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(Original post by annabel_gilmour)
I need to simplify

tan(x)*√(1-sin⁻²(x))

the only two identities I can use are tan(x)=sin(x)/cos(x) and sin²(x)+cos²(x)=1 (these are the only identities in the specification of the course I’m studying)

How would I get rid of the square root?
Is that expression written correctly, because 1-\frac{1}{\sin^2(x)} is negative for real x?
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S.78_t
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(Original post by annabel_gilmour)
I need to simplify

tan(x)*√(1-sin⁻²(x))

the only two identities I can use are tan(x)=sin(x)/cos(x) and sin²(x)+cos²(x)=1 (these are the only identities in the specification of the course I’m studying)

How would I get rid of the square root?
The square root is equivalent to the power of 1/2
So it is tan(x)*(1-sin^-2 (x))^1/2
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annabel_gilmour
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(Original post by 15Characters...)
Is that expression written correctly, because 1-\frac{1}{\sin^2(x)} is negative for real x?
I don’t know I’ve typed up exactly what the textbook says but it’s a new textbook and I have found some mistakes as I’ve been going along. The answer in the back is sinx...
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annabel_gilmour
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(Original post by RDKGames)
From the identity sin^2 + cos^2 = 1, you can notice that you will get \sin^{-2}x if you proceed to divide both sides of it by \sin^2 x.
I’m probably being thick but can you clarify what you mean by both sides? It’s an expression so there’s only one side I think
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davros
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(Original post by annabel_gilmour)
I don’t know I’ve typed up exactly what the textbook says but it’s a new textbook and I have found some mistakes as I’ve been going along. The answer in the back is sinx...
Are you sure the question isn't \tan x \cdot \sqrt{1 - \sin^2 x} ?
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annabel_gilmour
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(Original post by davros)
Are you sure the question isn't \tan x \cdot \sqrt{1 - \sin^2 x} ?
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this is a picture of the textbook - it could be a mistake though?
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davros
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(Original post by annabel_gilmour)
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this is a picture of the textbook - it could be a mistake though?
Well if you write tan x = sin x / cos x and then take the sin x inside the square root (so it becomes a multiplier of sin^2 x you can see that something strange is going on
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annabel_gilmour
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in

(Original post by davros)
Well if you write tan x = sin x / cos x and then take the sin x inside the square root (so it becomes a multiplier of sin^2 x you can see that something strange is going on
Shall I just leave this question then?
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davros
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(Original post by annabel_gilmour)
in


Shall I just leave this question then?
To me it just looks like a misprint so yes

Is anyone else in your class trying the same exercise?
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annabel_gilmour
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(Original post by davros)
To me it just looks like a misprint so yes

Is anyone else in your class trying the same exercise?
No - I’m self teaching so it’s just me!
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