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Let the function bijartive: (16)R $ R be delined by f(c)Prove that the functin &...

Question

Let the function bijartive: (16)R $ R be delined by f(c)Prove that the functin &

Let the function bijartive: (16) R $ R be delined by f(c) Prove that the functin &



Answers

Show that the functions $f$ and $g$ are identically equal. $$ \text { Show } \sqrt{16+16 \tan ^{2} \theta}=4 \sec \theta \text { if }-\frac{\pi}{2}<\theta<\frac{\pi}{2} $$

In this problem of relation function F G and H. B. The function from our to our. So here F G and H are the function from our to our, we have to show that F plus G of H is equal to F. O. H. And this will lead us, so we have to prove this and this is the first proof. And now we have to do another proof and another age F multiplied with G. Of the O. H is equals two. F. O. H multiplied with G. O. H. And now all I defined from Ottawa. So here first we are taking left hand side, so taking left hand side alleges. So this would be now we have to prove that this is equal to right hand side. So this age F plus G. So this would be F plus G of H and this is equals two F plus G. So this will F plus G. Of this can be written a check. So this will be a checks. And now from here we can write it, this is equal to f of a checks. So this will be F. Hx. Actually, so this is F H X plus G. Hx. And we know that S H. X can be written as fo fetch. So this would be F. F. S. And G H X can be written a goth G of H. So here we say that left hand side is equals two right hand side. So we can write, it has F plus G. Of H. Is equal to this hand side. So we can say that left hand side is equals two the right hand side. So we can say that hands group and the city proof. And now second part. Second part says that F multiplied with G. Of H. So again taking left hand side, taking left hand side. So by taking left hand side, we're taking here, F multiplied with G. Aw fetch. So this would be F multiplied with G. Of which. This can be written Sf multiplied with G. And H can be written checks. And now from here we can write it as F. Of a check. So this will be F of paychecks. So this would be F. Of X multiplied with gov checks and all are different from our tour. So we can do an operation here. So he had this would be no. This can we get an F. Of X. So similarly from here we can write it as this is F. Or fetch. And now this age multiplied with this can create energy of edge. So here from we can see that electricity equals two averages. So we can say that left hand side is equal to the right hand side. So that's why we can say that hands fruit and we can write it as F multiplied with G. Go fetch is equal to F O. H. Multiplied with G O. H. So this is the proof.

Hello. So our test today is to validate if this expression is the same as that expression. So let's get started. First of all, we can see that we can factor out the 16 and we're left with one plus 10 square data. Everything in the square root and we keep the right side the same so force you can data. Now we can separate the square root into two different expression. So 10 for second data. Now, the square root of 16 is four, right? And also there is a trigger biometric identity as follows. Second squared data equals one plus 10 square data. And when you look at this in here is the same as this one, right? And since we have established that this expression is the same as this function right here, we can say that Oh, it's the square root of second square. Data equals four second square. I mean, second data. And so the square root in the square, they canceled out. So we're being left with Second data equals four seconds data and that's it.


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