y(x)=4/(1+tan^2x)-3

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Originally Posted by john1999

y(x)=4/(1+tan^2x)-3

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Hint: replace tan^2x with sin^2x/cos^2x and see where it takes you.

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Originally Posted by ebaines

Hint: replace tan^2x with sin^2x/cos^2x and see where it takes you.

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Didn't help

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Originally Posted by john1999

didnt help

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What did you get? After making this substitution try multiplying numerator and denominator by cos^2x.

I know to identities this has just thrown me to the deep end

I got it down to y(x)=4cos^2/(1+(1/cos^2x)-3

no one can help?. I put it in wolfram and it gives y(x)=1-4sin^2(x)

any help on how to get to there

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Originally Posted by john1999

i got it down to y(x)=4cos^2/(1+(1/cos^2x)-3

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I think you made a mistake - what happened to the sin^2x term in the denominator?

Substituting :



Now multiply both numerator and denomninator by cos^2x:



You should recognize that , so this becomes . Now if you want you can subsitite to get the Wolfram solution.

yeah my mistake was when I multiply sin^2x/cos^2x by cos^2x would not that cancel out the cos on the denominator?

what program you use to write your equations?

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Originally Posted by john1999

yeah my mistake was when i multiply sin^2x/cos^2x by cos^2x would not that cancel out the cos on the denominator?

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yes it does, leaving the sin^2x term..

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Originally Posted by john1999

what program you use to write your equations?

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LaTeX - it allows for embedding math equations into questions and responses. You can learn about it here:
https://www.askmehelpdesk.com/math-s...las-50415.html

yeah agreed so for my information in the denominator

the sin^2x/cos^2x was multiply by cos^2x/cos^2x to leave sin^2x which makes it

4/1+sin^2x

then multiply that again by cos^2x/cos^2x

to get 4cos^2x/1+sin^2x+cos^2x

in your example where did the +1 go

Where did the 1+ go on the bottom?

?

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Originally Posted by john1999

yeah agreed so for my information in the denominator

the sin^2x/cos^2x was multiply by cos^2x/cos^2x to leave sin^2x which makes it

4/1+sin^2x

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No - what I did was this (leaving the -3 term off for simplicity):



I hope this is clear.