My thinking: tan(x) = sin(x)/cos(x), so sin(x)/cos(x) = t sin^2(x)/cos^2(x) = t^2 Rearrange for cos^2(x)
But I was wrong... Help?
You know... why not just draw a right-angled triangle with an angle x, adjacent side as 1 and opposite side as t ... hence use some simple trig to express cosx in terms of t, then square both sides. This can dodge your issue with identities altogether, but since that's what you're struggling with, I suppose you should try and overcome it.
Alternatively, Janej77's approach of using 1+tan2x≡sec2x cleans this up nicely.
You know... why not just draw a right-angled triangle with an angle x, adjacent side as 1 and opposite side as t ... hence use some simple trig to express cosx in terms of t, then square both sides. This can dodge your issue with identities altogether, but since that's what you're struggling with, I suppose you should try and overcome it.
Alternatively, Janej77's approach of using 1+tan2x≡sec2x cleans this up nicely.
Yes but why not let the poster carry on with their method first? It's not wrong ...
Yes but why not let the poster carry on with their method first? It's not wrong ...
I'm not saying they should stop doing their method... I'm just saying there are better alternatives, and since you're already helping them with their approach I had no comment on it...
I'm not saying they should stop doing their method... I'm just saying there are better alternatives, and since you're already helping them with their approach I had no comment on it...
I know there are other ways but I think it's better to let the OP complete their way and THEN advise them.