Plus sine squared theta, for any given theta, The unit circle definition, I know what cosine squared theta To think, hey, is there some identity forġ plus sine squared theta? But this is reallyĪll about rearranging it to realize that, gee, by What is this going to be? Well you might be tempted,Įspecially with the way I wrote the colors,

Make it this way- plus 1 plus sine squared theta. Squared theta plus 1 minus- actually, let's Well what's sine over cosine? That's tangent. To- you could view this as sine theta over cosine Squared theta over- this thing is the same thing asĬosine squared theta, we just saw that- overĬosine squared theta, which is going to be equal

That 1 minus sine squared theta is the same thingĪs cosine squared theta. Squared theta, all of that over 1 minus sine squared theta. Theta times cosine theta, well, that's just going to beĬosine to the fourth of theta. Simplify to cosine theta times cosine theta times cosine Squared theta times another cosine squared theta. The cosine squared theta, then I think I'm The former because this is a more complicatedĮxpression. We could either replace thisġ minus sine squared theta with the cosine Theta is equal to 1 minus sine squared theta. Squared theta from both sides, we get cosine squared Theta plus sine squared theta is equal to 1. Of the unit circle- is that cosine squared So how could I simplify this? Well the one thingįundamental trig identity, this comes straight out Minus sine squared theta, and this whole thing timesĬosine squared theta. Then tan^2 - 1 should theoretically be 0, I know this isn't the answer, but you can see that the 1 in tan^2 - 1 can't be ignored, it's not the 1 from the calculation of tan^2, so how can the simplification of tan^2 wipe out this 1?Įxamples simplifying trigonometric expressions. How is this possible? tan^2 is equal to sec^2 according to the calculations, they're just ignoring the one at the end of that original argument we're trying to simplify, like it wasn't there. Then somehow it says therefore tan^2-1 = sec^2 so it replaces the entire first argument with sec^2, completely ignoring that 1 we were supposed to deduct from tan. So sin^2/cos^2 + cos^2/cos^2 = 1/cos^2 and 1/cos^2 is sec^2 << still following The solutions tell us to divide both sides by cos^2. Tan^2 = sin^2+cos^2 = 1 << this we can agree on Start by simplifying the tan^2 theta angle

We must simplify (tan^2 theta - 1) <<<< note the 1 within this argument, we're taking an angle, and deducting 1 How is tan squared less 1 = secant? Each question for this section uses this central calculation to simplify the calculations, but it makes no logical sense

Calculus trig identities cheat sheet