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Solve the equation on the Interval [0, 2n). secx- [ = tanxThe solution set isI6...

Question

Solve the equation on the Interval [0, 2n). secx- [ = tanxThe solution set isI6

Solve the equation on the Interval [0, 2n). secx- [ = tanx The solution set is I 6



Answers

Find all solutions of the equation in the interval $\left[\mathbf{0}^{\circ}, \mathbf{3 6 0}^{\circ}\right)$. $$\tan x=1$$

In this question, we have to find all solutions off the grid. Sec X glows Dan Eggs equals one and into a lot x greater than an equal to zoo x less than two to buy. No, we know that second school to one upon Cossack. So we put here one upon Cossacks and 10 x equal Do sign x a phone call. Thanks. They called one So you can write like that one plus sign Eggs equal toe cause eggs. Now it's squaring both sides. Then we get one plus to sign Eggs blows sine squared eggs He could toe cause Squire eggs. Now we know that the Tekken American Identity, which is scientists Car explodes Coast Correct school toe one So you can write like that cause square eggs equal to one minus sign. It's quiet eggs Now We put that value here and we get one plus two. Sign eggs plus sign Squire eggs. Equal toe one minus sign. Let's go ahead. Eggs? No, we ate Sinus quite eggs from the both sides, and after that we subtract one from the both sides. Then we get two signs. Choir eggs, blues to shine eggs equal to zero Now we take TCF, which is to sine x Break it sine x plus one equal to zero. Now you can see that to sign eggs either sign act to sign Mexico to zero so you can say sine X equal to zero. Oh, sign X plus one could do so you. So we subtract one from the both sides and we get sine X equal to negative. What? Now we know that sign Mexico to zero when x equal to zero and, for example, toe by and here Sign ax, equal toe Negative one. So we know that when x equal toe 5.35 point two When then we get negative one. So here X equal to zero t pipe on to and fyi, eighties old final answer.

In discussion. We have to find all solutions off the question. Dennis Dennis. Square eggs. Okay, Equal toe sake. Eggs negative one and into rallies. Eggs greater than an equal toe. Zero eggs. Less than two to buy. Now we know that 10 x equal toe sine x upon Cossacks and second school toe one upon Cossacks. Now we put that value here and we get sign Square eggs upon cause squired X equal toe one upon calls eggs Negative one. Now we simplify this sign. Square eggs upon go to square eggs Equal toe Here is the like denominator, which is caused eggs and new militaries One negative cause eggs Now we multiply. Call sex to the both sides Then you get sane the Squire eggs upon cool tags equal Do one minus cause eggs. Now we have to multiply both sides by Cossacks again and we get sign Square eggs, equal toe calls eggs negative cause squared eggs. Now we subtract. Sorry, Ed cause square eggs to the both sides. Then began sign Squire eggs. Blood cause square eggs equal to go sex And here we know that it is a technocratic identity which is sign Squire eggs plus go to square eggs. Equal toe one. So now we put that value here and we get goes X equal to one. So we know that here Cossacks equaled one. So cause eggs value is one so x equal do zero. Then we get one. So x equal to zero is over. Find Lanza.

We've been contingent x equals -23. With the help of our unit circle. We're going to determine how many degrees that is. Tangent of X. Is signed over. Co sign sign is in my Y position, coastline is in my exposition. So we're going to be looking at it this way we only care about the top number because sign is opposite over high partners, coastline is adjacent over high Partners. So the bottom number on those right here is both the hypothesis, but tangent is opposite over adjacent. Which means I don't care about the Ipod knows. So we're going to focus on the top numbers. Sign is in the exposition or the Y position call sign is in my exposition, which means I want to be looking at it this way. Since it's the -123, that means I need my sign value here. The top number of my sign value to be a square 23 The top value. My co sign needs to be a one and one of them has to be negative because I have a -23. We get that at 120°.. I am square 23 and one and a negative. And we also get that at 315°.. Where to three and a one. And it's negative. So tangent X equals negative square 23 at 120 degrees And 315°..

Okay, So recall are falling identity that is seeking squared effect minus tangent square. Two bucks is equal to one. And now we can factory us into a sequence of X most tangent of X times. Sequins of X minus vengeance of X is equal to one. So we know that sequence plus tangent is equal to one that's are given. So we have that Speaking of acts, when this tangents relaxes, you go to one. Okay, so now let's add this equation to this one. So we have regions of minus tangents of axe. Is it with one? So I didn t Together we get two chickens of that physical too. The lining right to we get that sequence of X is equal to one. And when is seeking a vaccine which one? What actual in co sign is equal to one so that that X is equal to girl. Good


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