Example 6 (Part - 11) - Applications of Trigonometry, Math Video Lecture

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to trigonometry part 11 is brought you
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sure that you have watched part 1 to
part 10 we'll take some examples you can
find the value of sine 8th inning by
costs agree with you what we can do here
is the thing that comes to our mind is
if you can convert this into sine of
course already convert this into saying
any other things possible so let me try
to convert this into cos that cause
cause I can cancel so I can write sine N
18 degree by costs and it is nothing but
sign of issues of 18 and right 90 degree
minus n utility same thing right if you
say 18 or you say int - I know the same
thing by a cosine equal sine 90 minus
theta is nothing but cos theta becomes
cos theta theta is same dignity Y or
cellular and this becomes very simple
sign e 18 becomes sine of 90 minus M
into y because I'm making both costs if
I want to make both sign that ever
doable so let me write this way this if
we sign 18 degree by age it of course I
do si
cause all 90 degree minus in any way
cause of 90 minus theta is sine theta so
this becomes sine theta theta is
infinity listen so anyway sign it
immediately cancel you get one any of
the approach you get one
I think even convert cos to sign on sign
into first let's say for example
tan 2016 by God 64 degree almost similar
to what we have done last case so we can
save tan 26 degree by God 64 degree here
also I'll write 60 26 everything but 90
degree minus 64 my course is steeper so
tan 90 minus theta is nothing but cot
theta is cod 64 by court receiver and
this becomes 4 where is it because we
know that 26 plus 6
is 90 so big songs which will take a
little difficulty she caused 48 minus
sign 42 the author you see 48 plus 42 is
90 so we can somehow cancel this so let
me convert this cause underside so light
cause 48 earth nothing but cos of 90
degree minus 4 minus sign what
why because cos 90 minus theta is sine
theta so this becomes sine 4 into VD
minus sign for me and this becomes 0 and
that is - where is equation he also ABC
31 + 15 is 90 we know that Kozik we can
remember into say so well convert let's
is causing into sake so this I will get
nothing but Kasich 31 I write in instead
of caught the 13 has a 90 degree minus
59 degree - second led why because I
wanted to convert this into sec this is
nothing but sec 59 degree minus 6 you
name and that is nothing but soon we
will take home example this is a little
tricky 1048 10:23 1042 and times sister
you defined the bath you know that tan
into cot is good to 110 he tend to
Cartersville to 1 we know this valance
try it because tan theta is built upon
my corner also if you see that there is
48 degree this is fortunately the sum of
this two is windy so we'll make this has
one pair this is 23
this is 67 found this in the other 19
still makes us bear swelligant and 48
degree in two and for nearly one pair
do 10 23 degrees into ten sixty seventy
one pair right now we know that can
Endicott is equal to one
I can easily convert this into cotton
because C tan 48 will become caught for
it why because tan 14 when I say it and
I in divine is 40 to me because 48 is
nothing but 90 minus positive this
becomes caught caught into tan becomes 1
here also when I say tan 23 I can make
this as nothing but tan 90-87 that
becomes cottage 7 Koren term becomes
more and that is why I am proved in this
fashion so I'll write this as nothing
but tan off my G degree minus 42 degree
into tan 42 degree correct listen to tan
off 90 degree minus 7 degree into 10 67
degree this becomes tan 90 minus 42 that
is caught 42 into and particle into this
becomes caught 67 into tan 67 while time
90 minus ETA is caught it'll caught kita
into tan theta where theta is same
becomes one here's a cot theta into tan
theta where theta is sin becomes so this
becomes 1 and that is what we are
supposed to correct here what we have
done we have observed that 48 plus 42 is
equal to 19 when if you press 67 to 90
so we have formed these two pairs we'll
take our example cos 30 age into cos 52
minus sign for didi you see here if you
see 38:52 is one pair 3852 is one so
what we can do it you can convert either
all to sign or alter course so let's
convert all to sign to convert this to
sign up right in the power 90 minus
theta
spell right 30
has nothing but sine of 90 degree -
really here this also caused off should
have 52 else a 90 degree - correct
degree and this sign I will keep it in
sign only why because currently we are
converting everything to the sign form
cause 90 minus theta becomes sine theta
that is sign reading here of the COS 90
minus theta becomes sine theta
there is sine 30 degree and from this
ship you subtract sine 38 degree minus
or sine 30 degree in to sign it so if
you see both are same fifty two thirty
eight thirty foot sign this becomes Z
very simple because either convert
everything to sign or I didn't do cost
we divide something or subtract
something make sure you convert
everything into one ratio either all
side or all the question says if tan
two-way is going to cut immensely via to
is exiting a way to find Lago so here is
what we can do see caught and tan we
cannot compare so either let's convert
this also into cot both into cot or both
you tan so let's convert both into God
so converting this into car what we can
say tan 2 is nothing but court of 90
minus 2 we got it time to waste nothing
but caught 90 minister and this is
already in the cotton so this is nothing
but God II minus 80 million now since
both are in cart
I can compare so what I will get 90
degree minus 2a is equal to ka minus 1
ml ideally or I will get 3a is equal to
90 plus 80 is equal to 1 not eight or
like it a is equal to one not a by feed
against 36d correct and two way if you
see there is 3272 for a c2 and as I
equity and then speaking
see this is given two ways equal to
equity angle and that is the reason why
we could convert this into this fashion
had to have been an out to high angle we
could not we could not use this formula
because when you say and theta is equal
to caught up 90 minus theta theta has to
be greater than 0 and less than 90
degree that is theta has to be an acute
angle since two ways an IQ angle we
could use this time to weigh is going to
court 90 minus 2 8 they got both caught
both I caught we then compared cheetahs
and we got is equal to 36
mumbles happen if pani is good to caught
be here to do that a plus B is got my
degree similar to the last question here
also is his card hissed and we can
compare so let's convert this into court
Tan a is nothing but caught of 90 minus
V and this is equal to cottony he went
right since without God I can compare
this this 90 minus a is equal to B or I
can say a plus B is equal to my in
cheating it and that is what I have to
do and that is masked very simple once I
write made it God may God dance let's
take for example the question says if
sake for a is equal to cosec a minus
20db wherefore is acute since 4 is acute
I can use some formula find an angle
again same thing we have to convert in
kazakh form right both side kazakh and
since for a is a cute i can say that
sick poor is nothing but cos say 90
degree minus 4 I can write it correct
and this is nothing but Kasich a minus
20 so if I compare the angers I get 90
degree minus 4 a is equal to a minus 3
degree or I get a minus 4a take this
side you get five years equal to 90 plus
20 is 110 degree or is equal to 22 you
beginning and that is my answer since 4
is acute angle given you can use sick
for a is going to cause a 19-4 it looks
like cos it compare the theta that the
question see is take a B and C are
interior angles of a triangle you have
to show their sign B plus C by visible
cause you see the first thing that comes
to our mind when we see that a plus B a
B C our angles of a triangle that is a
plus B plus C in the correct now since
we're talking about a by 2 B plus C by 2
let's divide this by T yourself so what
we get a plus B plus C by 2 is nothing
but mind killing you're talking about
because C vitamin D by 2 bits separate
the song so what will get B plus C by 2
is nothing but 90 degree minus C by this
is my equation up there this is same as
this so it has a Y to it healthy Plus
event that means this equation can be
fulfilled was correct so we have to
prove that sine of B plus C I do so like
sine of B plus C by 2 will be equal to
sine of 90 degree minus event
why because V plus C by 2 is got no
degree in medicine now I've signed off
90 degree minus a by 2 is nothing but
cos off even and that is what we have to
put you know correct if you go by the
reversal method also sine B plus C by 2
is going to cause a by 2 if and what is
something to sign will becomes 90 minus
e by 2 that is B plus C is greater than
or 80 minus e by 2 you have this great
answer that's here
the question signs expressed sign 67
plus cos 75 in terms of trigonometric
ratio of angle between 0 and 45 degree
so the question says is a 67 you
expressed in such a way in sine theta
plus cos theta anyway we're all this
theta 1 theta 2 right they are all
between 0 and 40 what we can do you will
say 90 minus 17
so sine 67 I can say everything but cos
off or we can say this is nothing but
alike sine 67 is nothing but sine of 90
minus 20 feeling correct 67 inside 90
minus 23 is nothing but cos 23 and this
23 is between 0 to 45 first part is done
similarly costs 75 I can write nothing
else
cause of 90 degree minus 15 degree and
this is nothing but sine 50 degree and
this is also between 0 and 45 so now
what we can do again say that sine sixty
seven degree plus cos 75 degree this is
nothing but cos 23 degree plus sine 15
degree and this is my answer because
this Thetas are between 0 and 40 so
cushion asked or write this ratio in the
angles between 0 and per ticket and that
is what we have done thank you
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