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
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