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Find f,nrrJl,y)6oY + larctan(In(r' secx) + arcsin...

Question

Find f,nrrJl,y)6oY + larctan(In(r' secx) + arcsin

Find f,nrr Jl,y) 6oY + larctan(In(r' secx) + arcsin



Answers

Verify the given identities. $$\sin 3 x=\sin x\left(4 \cos ^{2} x-1\right)$$

Uh, second for X minus. Dungeon brown, Far X. And then we need to broken echo Jundullah, sir. Gun square, X plus Dunton Square X. Yeah, I was done with the left hand side. Now we know that we can ride this one. Echo Judah, second square, externally square minus something for this one Had a luncheon square extorting the square. Here we have a special formula for the I squared minus p square. There was again the I am honest be times I am. Just be now there from which again, our ego Judah second square, X minus Dunton square X and now attempts with, uh, second square x Stanton square x here for this one record up the one plus Dunton Square X recorded a second squared x isn't implies that the second square X minus the Dentyne Square X must equal to one. Therefore, this one here, where you go to one now Temps in the second square X uh, Stanton Square X. So doesn't exactly ico Judah. Right and sign how

We have to verify the relation that four sign ICS course Square X is equal toe sine three X plus Sign. Next, starting with the right hand side will get using the expansion. For you'll sign a sign Be This will become So Sign a plus B that is three X plus x, divided by two course off three x minus excavated by tool, which will be equal toe. So sign two X multiplied with core sex, which will be equal to two multiplied with sine x course. Six multiplied with Koszics, which will be equal toe four sine X cost Square X, which is equal toe the left hand side and hence the identity is verified.

We need to verify the identity that costs. Three X is equal to course off X multiplied with one minus four sine squared x, starting with the elegies. Weaken right. Cost three x as equal to cause off. X plus course off two x, which will be written US equal to to cause X cost two x minus course off X minus two x. This is again from the expansion identity that to cause a Cosby is equal to cause off a plus B class course off a minus bi. Now simplifying this, we'll get Toby equal toe to cause X cost. Two x minus cause X, which will become equal toe cause 246 cause sex comin on to cause two x minus fund within the brackets, which will be equal to cause sex multiplied with two multiplied with one minus two sine square x minus one. Since we know the identity that cost two X is equal toe one minus one minus two sine squared X So this will further become classics common to minus four sine squared X minus one, which will be equal toe course six multiplied with one minus four sine squared X, which is actually equal toe the arches and hence the given identity is verified

This is problem number 20. Yeah, in which we need to verify that NTT one plus sick four X divided by sign for X place 10 4 X equal to concept for X. Okay, so we'll be just transforming our left inside in two right and side using some basic identity. So left hand side is one plus sick for X by sign for X place 10 Forex. Let us convert it everything inside in the course so this will be one plus sick four x men's one by cause for X divided by sign forex William. And as it is, bless sign for X by cause for X So in numerator it will be a simply cause for X plus one because four x on in denominator, it will pay cause for text sign for X cause for X plus sign for ICS. Okay, so let us Alright, It as a zit is cause for X developed by If it takes sign forex common, it will become cause for X plus one by course forex William And as it is so cause for X plus one by cause for X in two, this will be reversed. So reverse means this will cause for X will go in the numerator and this will be then this will be in the denominator. So this will be cause for extra Went by sign for X cause for X plus one cause for X cost for expedient canceled out cause for X plus one and cause for exports one will get canceled out. We will be left with one by signed for X And according to our reciprocal identity this will be call sick for X which is our right inside. Thank you so much.


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