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Question

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Answers

If $\tan (\alpha+\theta)=\mathrm{n} \tan (\alpha-\theta)$ then $\frac{5 \pi 120}{\sin 2 \alpha}$ is equal to (a) $\frac{1+n}{1-n}$ (b) $\frac{\mathrm{n}-1}{\mathrm{n}+1}$ (c) $\frac{2 n}{n+1}$ (d) $\frac{\mathrm{n}}{\mathrm{n}+1}$

In this problem the given equation can be read it on us and in Warsaw x minus one plus cotton balls of x minus one. Yes done in loose off X plus one minus down in Los off explain this one equals two. Signing rules off four by five. Yes causing worse off three lifelines, You know tangibles of express card and most of expire by two. These two together pick up bye bye to now we have Bye Bye two plus the standing words of my understanding words of B just given us done and worse off a minus B which is express one minus X -1 divided by one plus into the Express one into X minus one. This is equals two sandals or fall by virus dan goes off four by three and cost ones of three x 5 is also planning worse off four by three this becomes again 10 words of a place. Standards of the standards of E plus B Divided by 1- in to be just four x 3 and two more likely comes us and and worse off minus 24 months seven. No, This becomes why by two plus this is done and worse off. You see that X and X gets canceled. We get to develop that X plus one expense one is X squared minus one. It's too big square. Yes. Turn and worse off -2457. Taking down both sides stand off by very to plastic ties. Got a story to so this is my sorry minus court of three to this is minus carter Bannon loss to buy X squared. This is taking And we have -24 x seven. This negative and negative gets canceled can be rewritten as caught off, caught in both. X squared minus two. Use equals to 24 x seven. Are we get X square equals two 48 x seven Or we get x equals two. A little 48 x seven is plus minus four road 3 by oh don't seven that's all.

So for this problem because we see that our expression that were given contains only tangent terms. We know that we are going to be using either the angle some or difference identity for a tangent. And so in this identity we have a plus sign in the numerator and a minus in the denominator. So this is going to correspond to our angle some identity. I'm so this identity tells us that the tangent of a plus B is equal to the tangent of a plus the tangent of beef divided by one minus attention of a times tangent of beat. And so when we compare this to the expression that were given in our problem, we can see that angle A is going to be five data an angle B will be six data. So when we plug this in on, we get this will reduce to the tension of a What we said was five feet up close B, which is six data, um, or we can simplify further to the tension of 11 thing

E think given expression as a single expression. The giving expression is showing you real bet Dan minus Don't be. Don't do it by one place down fall Can we? Don't this done? But I felt minus Peter No come back, Tell upside or this identity were they given expression ticket and by crystal White data and data include to Tito. Hence we can join Given Expressionists Don't by a veto minus two veto crying in this John Peter.

On the first part of the question. We have 10 60 day Rippner stand to 25 degrees, not 10 60 degrees for three, plus 10 to 25 degree. Which one? Now? For our bill. The question we have done to it from degree which cannot next. 10 16 plus 2. 25 Mhm. So wear toe former for 10 A plus me. You teach government less than me. Never one minus. And this good and be that is called a road three plus one development that one minister three.


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