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# C3 quotient watch

1. 1) given that

y= (1+tanx)/(1-tanx)

where tanx does not = 1
show that dy/dx is always positive

I've differentiate and got (2sec^2x)/(1-tanx)^2

but not sure how to prove that it's always positive
2. (Original post by ihatePE)
1) given that

y= (1+tanx)/(1-tanx)

where tanx does not = 1
show that dy/dx is always positive

I've differentiate and got (2sec^2x)/(1-tanx)^2

but not sure how to prove that it's always positive
Probably more obvious if you transform the fraction into another form.
3. (Original post by ihatePE)
1) given that

y= (1+tanx)/(1-tanx)

where tanx does not = 1
show that dy/dx is always positive

I've differentiate and got (2sec^2x)/(1-tanx)^2

but not sure how to prove that it's always positive
In the numerator, you have squared and in the denominator, you have squared , so what does that tell you about the signs of the numerator and denominator?
4. (Original post by ihatePE)
1) given that

y= (1+tanx)/(1-tanx)

where tanx does not = 1
show that dy/dx is always positive

I've differentiate and got (2sec^2x)/(1-tanx)^2

but not sure how to prove that it's always positive
What happens to a negative quantity when you square it?

Edit: overlapped withDesmos
5. (Original post by Desmos)
In the numerator, you have squared and in the denominator, you have squared , so what does that tell you about the signs of the numerator and denominator?
Thanks xox

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