L15 : Example-5 - Inverse Trigonometry Maths, Class 12 Video Lecture

hello friends this video on inverse
trigonometric functions part 15 is
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fear from exam before watching this
video please make sure that you have
watched part 1 to part 14 let us take
one more example so we have to write the
form simplest form tan inverse 1 minus
mu X square minus C now we have to prove
X equal to something
I hate we can see that is X mod of X is
greater than 1 so that means X is either
caustic or cause why because cos I can
constantly we generally have this range
so if you take kazakh this one cause X
square minus X that is cot square its
context 1 by context hundred panics so
you get tan tan form and you will be
able to simplify it if you take cos x
cos 4x minus 1 the sign 1 by sin will be
cosine you only to see you see let's
magnetic x-value Costigan so you
understand just this is the most
critical one extra cos theta assumption
is the most critical part here why we do
this because the first thing it was more
neck is greater than 1 this is in
default closet almost if you take kazakh
this comes out to be 10 and language
subtag you get something but if you take
x penticoff this comes out to be cos it
10% kazakh again it difficult for us you
have to again convert that into sine
from a tan form it will be all the
complex but just because the quotient is
to simplify this so we take x 30% ago
so this we come and square and visual
log posit square one right
and this becomes tan reversal op Kasich
squared theta minus 1 is 1 by hot
kingdom this is nothing but tan inverse
of tan theta tan has a plan theta is
nothing but you can say X going to cosec
theta you guys cost of more so and there
is a simplified form of time inverse of
1 minus root experiments but why how we
have done we understood the cushion
properly and then then we found that X
is equal to cosec theta is the best
replacement convert this improves next
let's take one for example they will
simple actually
so if you see one root of one minus cos
x by 1 plus cos x we convert the center
can form our province saw so if you see
this part again
where's 1 minus cos x is sine square X
by 2 disfigure and 1 plus cos x is
nothing but to prosper expect this also
being correct so if this becomes so if
everything is a decision anything in the
loop this is knowing that having a
bigger over here so this becomes tan
diversity you can say sine squared x
squared would cost for X by 2 is tan
square X by 2 that is X tan inverse tan
expect only this expected based a purple
just because 1 minus cos x by 1 plus cos
x this we invited harm and 1 minus cos x
fingers this 2 sine square expected we
can do this little miles close yes
learning's was expecting plus it's bumpy
that is the bigger than minus this is
plus where X 19 so this becomes 1 minus
X 2 plus X this becomes sine squared X
by 2 plus sine square expecting and that
is the dealer whose next words so really
got plus you say plus this becomes
actually hospital we'll take one more
example
Tigers cause X minus sine X by cos x
plus sine X it also will just convert
this into tan form so this do that
divide this by cross cross cross cross
hook becomes 1 minus stamp and
understand this becomes cos x minus sine
X by dou X dou right leg for six years
sly mix line process what I'm doing in
this dividing book by cos x so this
becomes time worst 1 minus tan X by 1
plus you see this is nothing for a
formula you see we have suam la tan
inverse X minus y by 1 minus y21 +
explain this is nothing but tan inverse
of X minus this formula is similar to
this the only thing is the 0 of X we
have 1 it is to apply
we have 10 it's almost same spawn one so
this one like it right everything were
tan inverse 1 minus tan inverse thanks
understand what we have done
thank Rus 1 minus 10 X by 1 plus tan X
compare this with this formula n versus
X minus 5 by 1 plus X 1 and score
formula X this is nothing but 1 here and
Y is nothing but X so we got this s
inverse 1 understand was panics and
panniers 1 is nothing but PI by 4 and 10
in verse 10 is something but X so we got
PI by 4 minus X this is a simplified
version of the big form canvas cause
it's minus sine X Biosystems this PI by
4 minus X let's say come for example
tankers of X by E square minus X square
so here also we have to simplify it so
what we have to do when you put X is
equal to something this you see right X
this less than equal to this will give
you some sleep takes this is less than
equal to u that means X is nothing but
either a cos theta or is my because a
cos theta R mod is less than a because
cos theta ma 2001 and sine theta model
also visible so that is either two of
the possible functions correct from this
regard now if I put X equal to a cos
theta this becomes a cos theta and this
becomes a square minus a square cos
written a sine theta this is become cot
theta actually which we don't want you
want this to be in the form of tan
alright so if you put a sine theta will
get sine theta here and here it also get
vulnera sine square is cost sy
my father hist answer will get and so
we'll use this so let's say X is going
to any sine theta so what we'll get here
always it clida is nothing but sine
inverse X by so let's do texture to this
and it ends this becomes tan inverse off
a slightly by this point is P Square C
square theta this becomes tan inverse
off e sine theta by 1 minus sine square
theta cos square theta from a cos theta
e square minus e square sine theta
becomes a rule that becomes e possible e
cancelled sine theta by cos theta that
is tan inverse of tan theta the form
which we really wanted and this is a
liquid theta and theta is nothing but
sine universe XY e so this is my
simplified form of tan inverse X by a
square and that is sine inverse X /
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